Todd Archer of ESPN.com called that deadline "completely bizarre."
Archer added that if Romo remains on the roster when voluntary workouts begin, he could show up for those workouts and potentially injure himself. If that happens, the Cowboys would be on the hook for the entirety of his $14 million salary.
Additionally, if Jones is trying to buy time to work out a trade for Romo, it seems unlikely to succeed. It's hard to imagine teams will give up assets to acquire Romo when they could wait for the Cowboys to cut him. As Archer noted, "Reports out of Houston and Denver have said that the Texans and Broncos are not interested in trading for Romo."
As well, any team interested in acquiring Romo would likely want to have him learn a new offense well before the start of training camp. The longer the Cowboys don't make a trade, the more likely a team that is looking for veteran help at quarterback will turn elsewhere.
So if Jones has any leverage in Romo trade talks—and because teams know that keeping Romo as a backup next season isn't tenable for the Cowboys, Jones really doesn't have any leverage—it will only decrease as this saga drags toward training camp.
In the meantime, Romo is "contemplating whether he wants to continue to play" and potentially taking the time to "mull the offers from Fox and CBS," per Archer. Perhaps Romo will end this standoff by retiring.
If he continues his career, however, the standoff will inevitably end with what has always appeared to be the only logical outcome: The Cowboys will release him.