I just played the game last night, shut it down with no problem, started my computer up this evening, and now I'm receiving this error message:

Steam was unable to sync your files for Fallout: New Vegas with the Steam Cloud

It say's I'll lose progress or saves. Why did this happen? What can I do about it?

Last I heard, the Steam Cloud has been disabled on this game. You'll still be able to save locally with no problems. The only difference is that you'll have to copy your saves over if you ever reinstall windows.

Why is it disabled? Will it be re-enabled?

AFAIK it was disabled because it was wreaking havoc with savegames and .ini files. The game software wasn't playing nice with it and it was driving people that like to tweak their .ini files nuts. I doubt it will be re-enabled, but who knows?