I think I would pull the trigger on this one. As I see it:
Chauncey and Billups aren't much different. Billups is older, but he's a better shooter, and is a good passer. With Carmelo there, the ball won't be in a point guard's hands quite as much, anyway. Plus, Chauncey will have an expiring deal right before 2012, setting New York up well for CP3 or Deron (or potentially Howard).
The #1 picks aren't worth a whole heck of a lot, since they'll presumably be somewhere after 20th in the draft. Not a huge sacrifice there.
Wilson Chandler is a restricted free agent. They're not going to be able to sign him and sign Carmelo, so I don't see him as a major asset.
When you look at it that way, the only legitimate asset you're giving up for Carmelo is Gallinari. That's a fair swap, I'd say, especially since the team will have to say goodbye to Gallinari if they hope to sign a 2012 free agent.
Of course, NY should wait this out a bit to see if Denver caves at all, but if this is the bottom line, I would pull the trigger without any hesitation.