How much time? I don't see NCR falling apart if they lose the Mojave. President Kimball would be in trouble but NCR would not fall, hard times is likely. Its also a matter if time before the Legion falls apart when caesar kicks the bucket.
For one I'd expect a revolution or two, other than that I really see it as that they will lose a crapload of money due to their loss at the dam, with the loss of money they have to cut down on certain aspects, one being military, if the law is cut down then the less prosperous towns and cities will have the NCR law enforcement taken away.
When that happens then it's only a matter of time before someone with the ability to place words right to start his/her own faction and rules the town/city his/her way or until a raider band attacks the town.
With NCR being cut back a lot of land will be unprotected, with that follows raiders and other factions being born.
When the roads become unsafe for trading a lot of isolationism will happen and supply and demand will go down the toilet.
Then people will set sight on the good stuff, greed will overcome raiders and new factions as their mouths get watery from watching NCR's fun stuff.
At some point there will be war between NCR and these new factions, question is, can NCR handle them?
I'd say it's a 50/50, maybe and maybe not.
But if not then the lands will once again slowly be set back to square one.
Legion on the other hand, they view Caesar as their god, willing to give their lives for the man.
But can
Caesar die?
Sure enough the current holder of the title can die, but upon his death someone else will take the title and become the new Caesar.
Basically Caesar>Lanius>Lucius>Vulpes>et cetera.
If the manifestation of Caesar dies then the next in command will take his throne and run things his way.
I don't see Legion falling apart unless a future Caesar is completely incompetent and runs it into the grave or if another superpower finds and kills everyone of them or if 4 Caesar in a row is killed in a timespan of 1 year.
That's the way I see it. :shrug:
But I'd say that the NCR part is under a timespan of 5 to 20 years.