A loss in Sunday's divisional round game against the Seattle Seahawks should put him on it.
It may not be a popular opinion after all that Smith has accomplished: Coach of the Year in 2008; five consecutive winning seasons; winningest coach in Falcons history.
All of that was reason enough to keep him around before.
Not now that the expectations are raised.
After decades of futility, it used to be that just a winning season would be seen as an accomplished season. That one was by-passed in year one of the Smith era. Then, that of back-to-back winning seasons in 2008 and 2009. Then, that of back-to-back playoff appearances in 2010 and 2011.
He has led Atlanta from the abysmal franchise that it was before into the winning machine that it is today.
But where he hasn't led the Falcons, is to postseason success.
As head coach of the Falcons, Smith is 0-3 heading into this weekend's playoff matchup against the Seahawks.
That's despite having some of the most talented teams in the league assembled by general manager Thomas Dimitroff, who brought the the likes of Matt Ryan, Tony Gonzalez, Julio Jones and Asante Samuel to Atlanta since owner Arthur Blank hired him in 2008.
There were excuses abound for those three postseason losses:
Ryan was just a rookie in 2008's 30-24 loss to the Arizona Cardinals.
Ex-coordinator Brian VanGorder's defense was the reason the Green Bay Packers rolled over the Falcons 48-21 in 2010.
Then, it was ex-coordinator Mike Mularkey's turn to shoulder the blame after Atlanta's offense failed to score a single point in the Falcons' 24-2 loss to the New York Giants last January.
Now, Ryan is in his fifth season, while offensive coordinator Dirk Koetter now leads one of its most explosive offenses and defensive coordinator Mike Nolan one of its most opportunistic against even the best of quarterbacks.
Even better for the Falcons, they are the No. 1 seed after a 13-3 regular season, set to face a Seahawks team they beat on the road in 2011 and invite to the Georgia Dome—where Ryan is 33-4 as a starter—this weekend.
All of the pieces are in place for a Falcons victory.
And if the Falcons fail this time, there won't be anybody to blame but Smith himself.
All the pressure is on him: From the fans, from the media and, most importantly, from the front office.
And that's what winning in the playoffs is all about: performing under pressure.
Pressure is what separates the true contenders from the frauds. Those who are able to perform under pressure are those you want leading your team, the ones who crumble to it, aren't.
So far, Smith has proven to fall under the second category.
Sure, he's led the team to a 56-24 regular season record since joining the team in 2008, a record only bested by the New England Patriots in that span.
But trophies aren't handed out for regular season success. They're handed out for those who can not only make it to the playoff wall but break through to the other side, where the only trophy that matters awaits: the Lombardi Trophy.
In three of the past four seasons, Smith has come face-to-face with that wall, only to find himself incapable of breaking through it it every time.
And if Smith can't break through it this time, it may be time to consider that perhaps he never will.