Just encountered the same issue, some hours into the game (test purposes), on save no.38. So I decided to place the previous saves in a different folder (just in case) and keep just that particular one. Started the game, loaded save 38 and it worked. My guess? Might have something to do with the number of saves/filesize. Too many, perhaps?
Is there a threshold for how many saves can be used before this bug happens? I have around 50 save files.
Unfortunately I have no idea. In my case it triggered after approximately 13 hours, though I cannot pinpoint what caused it.
I do remember being inside the Basincreek Building and reaching the second floor. On this level there is a door which leads to a void (an oversight perhaps). This is exactly where I saved the game (save 37 at that point). Played several more minutes, saved near McCarran (38) and had to leave the game. Trying to load save 38 led to the bug.
I'm guessing it also might have to do with saving while inside the textures - opening that door inside Basincreek Building was never intended. I should also mention I had no mods installed.
There are numerous bugs in New Vegas, but this one is by far the worst I've noticed.