Elder Lyons is an idiot. Why is he sending his men into D.C? Its like sending a snowball into hell.
Because Lyons assumed the D.C. Ruins was where the Super Mutants were coming from, prior to the discovery of Vault 87. He thought the Super Mutants that were ranging beyond the Ruins were
leaving not arriving.
As for the NCR - Too Big, Too Fast.
Or perhaps it would be better to say the Post-Apocalyptic world is unable to support our modern concepts of a country. Even with the thousands of lives lost to the Legion and the Brotherhood, the NCR is still facing a Overpopulation Problem that will lead to starvation within a decade. That overpopulation also resulted in them seizing Hoover Dam in the first place, to generate the power needed for their own cities (Keep in mind, The Mojave's only getting the bleed off. All the juice is going back to California), and the Followers also remark that medical treatment leads to longer lives, which ultimately eat into the available supply of Pre-War Medicines.
The NCR is a bootstrap Civilization, using Pre-War advantages to jury rig a Empire. Their eyes are far bigger then their stomachs and unless they pull back and digest what they've already taken they'll explode. Or worse, turn to aggressive expansionism. The NCR could push deeper and deeper into the bombed out US, trying to outrun its own demise by seizing as much farm land, Pre-War Tech, Medicine, etc as they can get their hands out, but each time they do they become larger yet and cannot handle the constant strain.
One way or another, unless something breaks their way, the NCR's in a lot of trouble in a few years.