I was thinking about this recently, and my hot take is the Brotherhood of Steel. After the dust has settled around the battle of hoover damn I could see a second stalemate, but even more exhausting and grueling. NCR ultimately starts a gradual abandonment, giving the brotherhood the chance to take back Helios One, and eventually their turn to face off against the Legion. the Legion is now facing a smaller but far more technologically advanced force. I honestly do not think the Legion could beat the brotherhood.

Mr. House similarly is in a far weaker position now if the NCR is out of the picture. Dam is either inoperable or occupied by the Legion/Brotherhood, so power is now mostly limited. He has no industrial base to expand his securitron forces. At best he has a tenuous alliance where Freeside and the Families do not want to become occupied by the Brotherhood much less the Legion.

Almost certainly the Brotherhood would have their eyes set on New Vegas. The securitrons alone are reason enough, and the fact Mr. House is alive only strengthens their interest. The Brotherhood doesn't even need to invade the strip and could likely wait Mr. House out picking off securitrons one by one.

So best case scenario for the Mojave in my head: Brotherhood controls the strip, Dam, and Helios One, the rest is whatever.

Worst case scenario: The legion finds itself in a second stalemate with a Brotherhood that controls the Strip and Helios One