The scenario (please read as much as you can before voting, also the events of the Hunger Games Trilogy are not canon to this post, they do not happen at all):

NCR Rangers discover a series of portals in the Mojave, particularly the area around Goodsprings, and report this to the military. The NCR high command orders some robots sent into the portals for reconnaissance and they return safely. After hearing the reports of a lush landscape of fertile trees and large unmutated animals similar to that of what existed before the Great War they become intrigued and eventually are finally feeling safe about the portals. the NCR decides to send in a team of 20 rangers to set up camp and provide intel about the area. After a period of months the NCR learns that an entirely different nation exists on the other side, the nation of Panem. The Rangers give reports of Panem having extremely advanced technologies that would provide extremely useful to the NCR, fertile soil far superior for farming than what lies in California, vast water reserves, and ample reserves of electricity. They, however, also report the nation to being extremely hostile to it's own people. They report massive famine in the midst of plenty of food being produced, wide-scale blackouts despite being well energized, and droughts despite being surrounded by fresh water reserves. On top of that they report that every year each of the "Districts" were forced to send their children to be broadcast in a live arena. Despite this the NCR sends an ambassador and an armed guard to negotiate for the NCR to set up some farming settlements to provide food and to begin setting up water processing plants to supply water to California. Once found by  a squad of Peacekeepers they were arrested, sent to the Capital, interrogated, and tortured. Only one guard was allowed to live and was sent to the portal to tell the NCR of what happened. Not only that but the Ambassador was publicly tortured until he died and the ordeal was broadcast on TV.
  Enraged and greedy for the spoils that Panem held, the NCR quickly mobilized it's army to Panem and began setting up military bases along the east coast (on the outer regions of District 12) And ensue to declare war on the Capital. The war finally begins. (sorry it took so long, I'm bored and have been imagining this scenario for the past few days)
  NCR then makes the first move by invading the relatively unoccupied District 12 and quickly assumes control of the District. District 12 is now occupied by the NCR.
The Capital is highly offended by this and mobilizes its air force to bomb out District 12 (it's not like they cared much for it anyway) Thousands die. They then proceed to begin a bombing campaign on NCR bases and military fortifications.
 The NCR not realizing the air capabilities of the Capital quickly attempts to reorganize itself by heading north, until they stumble across the what appears to be abandoned District 13.
  A group of District 13 scouts report to their leaders that a large military force that isn't from the Capital is at there doorstep. They then proceed to watch the NCR carefully.
After D13 learns of the NCR intentions, they see an opportunity, the NCR could be effectively used to destroy the Capital, however they lack the air capabilities needed to fight back. They then send in ambassadors and negotiate a treaty, the NCR can hide in D13 and mobilize for an offensive southward into D12 and D6 and D13 will provide anti-aircraft support and some of their own aircraft to aid in the fight, meanwhile they use the war to show the people of Panem as a reason to begin a revolution.
Basically it all comes down to this: D13 incites revolts and decreases internal stability and the NCR fights the Capital in war with the antiaircraft weapons from D13 (and perhaps some more, and there own of course) And at the same time NCR Spec-ops try to plant the FEV into the Capital's water supply. With all this going against the Capital, can the Capital fight back and defeat the NCR-D13 alliance? Any thoughts on the Capital trying to invade California?

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And at the same time NCR Spec-ops try to plant the FEV into the Capital's water supply.

Considering the effects of FEV, and the stupidity of Peacekeepsers(hey lets only send 5 guards to keep watch at the giant dam." Half of the Capital gets mutated and the rest get slaughtered by the new super mutants with weird costumes on them.

100% For the NCR I guess the courier also doesn't get involved...that might make it too easy for the NCR

The NCR, Without a shadow of a doubt, On top of a huge army, that is generally effective and patriotic (for the most part), They have the Rangers, Each sporting military grade equipment and grueling training to be admitted, The NCR Army is also battle tested, surviving the harsh conditions of a desert war against a similarly dedicated army. The Peacekeepers, on the other hand, are bullies in white armor, trained to murder unarmed and malnourished civilians.

Ah, the civilians, How could I forget?, Each and every one of the inhabitants of the Districts hate the Capitol, And hearing of an invading army that brings democracy, freedoms and the rule of law to it's citizens would motivate them to throw their lot in with the NCR, Bolstering their Trooper numbers if the NCR decides to send them back to the Mojave to be trained as such.

The only advantage the Capitol has is it's air force, If the NCR could develop mobile AA Guns, The Capitol would fall with minimal effort.

Well since Capitol is used to fight starved, near to death people then I would have to side with NCR.