At this point, Jerry Colangelo and company must be praying that they will still have a healthy roster of 12 players by then.
Last week, we learned that Miami Heat stars Dwyane Wade and Chris Bosh would be forced to sit out of the Olympics this summer due to injuries. It only got worse yesterday, when Adrian Wojnarowski of Yahoo! Sports broke the news that No. 1 overall pick Anthony Davis will likely miss the Olympics after severely spraining his ankle during a workout this past weekend.
Of the 22 players that have been named to the preliminary roster, only 15 are healthy enough to play. Beyond Wade, Bosh and Davis, Derrick Rose, Dwight Howard, LaMarcus Aldridge and Chauncey Billups will all be rehabilitating injuries this summer instead of playing for a chance at an Olympic gold medal.
But, barring further injuries this week, the Americans will still enter the Olympics as the gold-medal favorites.
So, distract yourself from the free agency madness for a few minutes and check out one man's picks for Team USA.
This starting spot will inevitably come down to a two-man race between Chris Paul and Deron Williams, but CP3 should end up edging out D-Will.
In terms of pure point guards, you won't find anyone better than Paul. He possesses uncanny court vision, allowing him to slip passes to teammates that other point guards wouldn't dream of attempting.
CP3 finished with the highest PER and Estimated Wins Added of any point guard in the NBA this past season, proving that his value extends far beyond his ability to run an offense. Paul can knock down long-range jumpers just as easily as he can slither his way to the basket for layups, making him a dynamic offensive threat from anywhere on the court.
Team USA will need a strong, vocal leader at the starting point, and Paul's known for being just that. He's not afraid to bark at teammates for missing defensive rotations or blowing offensive sets.
Unless his diminutive frame puts Team USA at a major matchup disadvantage, expect Paul to be starting every game for the Americans this summer.
Kobe Bryant will roll over dead before abdicating his starting spot on Team USA to a younger player.
He may be turning 34 at the end of August, but as Bryant proved last season by nearly leading the league in scoring, he still has plenty of gas left in the tank.
Back in 2008, in the gold-medal game against Spain, Bryant was the one steadying Team USA's ship in the fourth quarter. When the Spaniards cut USA's lead to single digits, Bryant all but demanded the ball, willing the Americans to victory with their backs against the wall.
With so many other superstars on the roster, it's doubtful that Team USA will require such heroics from Bryant again this summer.
Still, it's an added luxury for the team to have a shooter in the starting lineup who never shies away from momentous, high-pressure shots. That's Kobe Bryant to a T.
Anyone who doesn't think Kevin Durant will be in Team USA's starting lineup clearly hasn't watched a single game of professional basketball since 2010.
Durant was the key cog for Team USA in the 2010 FIBA World Championships, averaging over 22 points per game—and he's only gotten better in the two years since. No 23-year-old should lead the NBA in scoring for three consecutive years, but Durant just did.
Scoring will unquestionably be Durant's greatest asset to the team, with his ability to get off a shot in the blink of an eye. That quick release gives him an offensive advantage over every other player in the world, including LeBron James (luckily, they're on the same team now).
That's not to detract from the other contributions Durant can make for Team USA. He's not too shabby of a rebounder, having averaged eight boards per game this past season, and has made a concerted effort to expand his offensive repertoire by getting his teammates involved.
Durant, unquestionably, is one of the five most talented basketball players in the world right now. As a result, he is a lock to earn a starting spot for Team USA this summer.
If LeBron James can even come close to matching the intensity he displayed during this year's NBA Finals, the rest of the world doesn't stand a chance.
King James finally earned his nickname this year by putting the Miami Heat on his back in the playoffs, bringing Miami a well-deserved NBA championship. James stopped drifting to the perimeter as frequently as in past seasons, recognizing his inherent advantage in the post.
LBJ often bristled about consistently playing power forward, but with the plethora of injuries to the bigs on Team USA's preliminary roster, the Americans will need James to step up and do it again this summer.
Equipped with his newfound post game, it shouldn't be much of a problem for James. He's always been an absolute menace on the glass, and when opponents send double-teams his way in the paint, James can methodically pick apart most defenses.
Since his last Olympic experience, all James has done is win three league MVPs, a Finals MVP and an NBA championship. Suffice it to say, Team USA can likely expect more in this go-around than the 15.5 points, 5.3 rebounds and 3.8 assists per game he put up back in the 2008 Olympics.
At this point, Tyson Chandler has effectively earned the starting center spot on Team USA by default.
Had Dwight Howard or Chris Bosh been healthy enough to compete this summer, Chandler's starting spot would assuredly be in jeopardy. But without those two, the NBA's reigning Defensive Player of the Year has this spot on lockdown (no pun intended).
Chandler isn't the sexiest name, but he's Team USA's only remaining healthy seven-footer. Assuming that the Americans end up in a gold-medal-game rematch with Spain, they will desperately need Chandler's size to battle the Gasol brothers and Serge Ibaka.
One thing Team USA won't be asking Chandler to do? Put the team on his back offensively. He will be there strictly for defense, deferring to other-worldly offensive options like Kobe Bryant, Kevin Durant and LeBron James routinely.
Having played with Carmelo Anthony this year and Chris Paul back in his New Orleans days, Chandler has experience teaming up with superstars unafraid to attempt 20-plus shots per game. For Team USA to succeed in their gold-medal mission this summer, Chandler's lack of offensive ego will prove critical.
I'll admit it: I'm one of the biggest Carmelo Anthony detractors out there. He is a volume-shooter who routinely takes off possessions (if not whole games) defensively.
That said, just like four years ago, Team USA will desperately need Anthony this summer.
During the 2008 Olympics, Anthony's ability to space the floor and knock down the international three-pointer (nearly two feet closer than the NBA's line) with regularity proved critical in the medal rounds.
Anthony can play either forward position for Team USA, and with a lack of conventional big men, the Americans will need all the versatility they can get this summer.
Like Durant, anything Anthony contributes beyond points and rebounds will be found money for Team USA. Don't be surprised to see him among the top point-per-game scorers for the Americans, as he was for the 2008 Olympic team.
With his fellow big men on the preliminary roster dropping like flies, Love is quickly becoming one of the most important members of Team USA.
For starters, despite only having four years of NBA experience, he is quite possibly the best rebounder in the league already (yes, even better than Dwight Howard).
Without Howard's presence this summer, the Americans will need Love's fundamental footwork and scrappiness on the boards to stand a chance at the gold medal.
And unlike Howard, Love has a perimeter shooting game to match. The UCLA product has averaged over 37 percent on his three-point shots over the course of his career, giving Love a huge advantage in international ball, which tends to favor stretch-4s.
Love never carved out a huge niche with the 2010 FIBA team, playing a total of 79 minutes in nine games, but expect him to have a much larger role for Team USA this summer.
Somehow, after being traded to the Nets, it's almost as if NBA fans forget just how good Deron Williams can be.
Like Chris Paul, Williams will attempt and complete passes to teammates that few other point guards could even imagine.
He is a pass-first, score-second player like Paul, but he has shown an ability to pour in the points when necessary.
Remember his 57-point explosion this past season?
D-Will played a huge role on the 2008 Olympic team, serving as CP3's backup and playing only 22 less total minutes than him over the course of eight games. He finished behind only Paul and LeBron James in terms of assists in the Beijing Olympics.
Four years later, Team USA will call for a repeat performance.
Russell Westbrook catches all sorts of hate from NBA fans for not being a traditional point guard in the mold of Chris Paul or Deron Williams.
You know what? Neither is Derrick Rose. And with Rose missing these Olympics due to the ACL tear he suffered in the playoffs, Westbrook will be expected to step up and fill that role.
Unlike Paul and Williams, Westbrook often goes into score-first, pass-second mode. When you're on a team with efficiency giants like Kevin Durant and James Harden, that mentality tends to result in a heap of criticism.
But just when you're ready to bury Westbrook for good, he goes off and explodes for 43 points, seven rebounds and five assists in an NBA Finals game.
The Americans will thrive with Westbrook's aggressive mentality pushing them to score until the lights go out. You can expect a few boneheaded turnovers and drives into triple-teams, but the benefits of Westbrook's game outweigh the flaws for Team USA.
Like Kevin Love, Griffin has effectively backed his way into a spot on Team USA by virtue of staying (relatively) healthy.
In only his second season, Griffin became one of the league's few players who averaged 20 points and 10 rebounds per game, proving his value as a franchise cornerstone for the Los Angeles Clippers.
But really, he's best known for his highlight-reel dunks. Beyond rebounding, that's what Team USA should expect to see most from Griffin.
After all, with his teammate Chris Paul along for the ride, how could the Americans not bring Lob City over to London?
Not to mention, the international game will really favor Griffin's flopping tendencies (kidding...sort of).
With Andre Iguodala's selection, we've gotten into the truly tough decisions. Really, this spot boils down to Iguodala versus Rudy Gay of the Memphis Grizzlies.
There's no doubt that Gay is the better scorer of the two, but Team USA already has Kevin Durant, Carmelo Anthony and LeBron James on the wing for that very reason.
Iguodala, on the other hand, earns his keep on defense. Like with Tayshaun Prince in 2008, Team USA will likely want to bring one lockdown swingman along to London, and the odds favor Iguodala for that reason alone.
This isn't to say Iguodala can't score at all. Team USA shouldn't encourage many long-range jumpers from Iguodala, but he did knock down a career-high 39 percent of his shots from three-point range this past season.
Instead, Team USA should only ask Iguodala to help facilitate fast-break opportunities, convert easy chances around the basket and frustrate opponents defensively to the point of no return.
This will be the toughest decision for Team USA, in my eyes. Based on the preliminary roster, it looks like this final spot will turn into a battle between Eric Gordon and James Harden.
In terms of playing styles, both players are actually pretty similar. Harden and Gordon are both sharpshooters who can also thrive controlling the offense with the ball in their hands.
Gordon had surgery on his right knee in February and only played in seven games at the end of the regular season, but I'm operating under the assumption that he will be 100 percent for Team USA training camp later this week.
What gives him the edge over Harden? He played for the 2010 FIBA team, while Harden was added to this 2012 preliminary roster only after injuries to other top stars.
With the Team USA selection show only a few days after the start of training camp, it's tough to imagine Harden surpassing a fully healthy Gordon, considering his past contributions. team.
But again, of all the picks, this is the position that seems most up-in-the-air four days removed from Selection Saturday.
When the Sacramento Kings' DeMarcus Cousins was added to the Team USA Select Team, it wasn't enough for him.
"I'm not going there (Las Vegas) just to practice," Cousins said in early June, according to the Sacramento Bee. "I can make that team."
Cousins' declaration may have sounded like pure hubris at the time, but it may end up turning out to be prophetic if any more big men on the preliminary Team USA roster succumb to injuries.
It remains to be seen whether the Americans can add a new player to their 12-man final roster this late in the proceedings, but if Cousins goes into training camp and dominates all the other bigs for the first few days, one can only imagine that Jerry Colangelo will be placing some calls to the International Olympic Committee later this week.
A brief explanation of why these three don't make the cut:
Rudy Gay: A great scorer, but not much else. Assume he will be competing with Andre Iguodala for one of the final spots, and Iguodala's defense should push him above Gay.
James Harden: Zero international experience. Added to the 2012 preliminary roster only after injuries to other top stars. Competing with Eric Gordon, who played in the 2010 FIBA tournament with Team USA.
Lamar Odom: Already withdrew his name so he could focus on the upcoming NBA season. Even is he hadn't, Odom had his worst season as a professional last year with the Dallas Mavericks.
Out with Injury: LaMarcus Aldridge, Chauncey Billups, Chris Bosh, Anthony Davis, Dwight Howard, Derrick Rose, Dwyane Wade