John Clayton of ESPN posted what appear to be updated salary cap figures for all 32 NFL teams today (hat tip to sleepy042 for pointing this out). They might not be exact numbers, but they are probably close estimates.
Here's what we know. The salary cap should be $120 million this year, and it is believed that every team will be forced to spend at least 90% of that amount (equal to $108 million). The Browns are listed as being $33.3 million under the cap. Doing some quick math, they would need to spend at least $21.3 million re-signing their own free agents, signing free agents on the open market, and signing their draft picks.
By a quick count, eight teams have more free space than the Browns at the moment.
I still think Jake Delhomme will be a quick cap casualty. His base salary is $5.4 million in 2011, so if you take that away, the Browns could be around $38.7 million. In that case, only two teams, Seattle and Tampa Bay, would have more free space than Cleveland. It's probably unfair to consider what-if scenarios, because there will probably be quite a few teams who cut players to ditch their overpaid salaries.