I'd recommend backing up your save files ahead of time.

1. Disable steam sync for new vegas
> Open steam, right click new vegas, in the updates tab uncheck the box that says something along the lines of syncing with the steam server hit okay, close steam.
2. Download and install FOMM
> http://www.newvegasnexus.com/downloads/file.php?id=36901
> It's all pretty self explanatory, tell it what you want, allow it to edit the .ini. It will find the game for you. If you're running with UAC or limited user you have to let it write to a directory you can write to. I created "My Documents\fonv\" for that
3. Launch and choose offline mode.

Post whether or not it works for you.