Assuming everything will go as smoothly as senior producer Jason Bergman seemed to suggest in his tweets here and here, owners of the Xbox 360 version of Fallout: New Vegas should be able to download the version 1.3 patch by "the wee hours of the morning."
Good news! The Fallout: New Vegas patch is rolling out on 360 tonight. Same changes as PC/PS3. As a reminder, the patch notes can be found here.
If you're planning on staying up for the FNV 360 patch tonight, it'll be a while. I wouldn't expect it until the wee hours of the morning.