I've looked at this many ways and I cannot find a way that the Legion will lose. They are more dug in, have grips on both sides of the river and are better prepared for the battle at Hoover Dam. The only shot anyone has of beating them lies with the Courier, but I don't see any reason for him not joining the Legion - they are the better faction afterall.
Taking the Courier out of the equation, NCR are doomed as they don't have the numbers present, the equipment ready and the soldiers they do have are drafts and poorly trained, not to mention they are losing their foot hold on the south east of the map. They have poorly secured their lands, as evident by deathclaws, casadores and radscorps, as well as raiders and fiends roaming freely around. Legion in their short time across the river have killed off almost all the pests plaguing the south side, never noticed how empty the place is?
House has no chance of getting back in the game without the Courier. Sure he'll get his chip back from Benny at some point - if whoever House sends doesn't spook Benny like the Courier did. But how will the replacement get through Cottoncove and into the Fort, then by all the security guarding the bunker all the while walking right past Caesar's tent. House is out of the game absent Courier.

Does anyone else have thoughts about Hoover Dam, absent the Courier?