It's hard to get exact numbers, but the two quotes from above are probably the best we have to go on:
- "Although the quarians had maintained zero population growth aboard the Flotilla quite successfully in the three centuries since their exile, their problem was the lack of spaceworthy vessels. They were unable to replace old ships as fast as they were losing them, and within ninety years, their population would be unsustainable."
- "It's the difference between sixty years and six hundred. For anyone alive today to see a sunset without a mask, we must take back our home."
The first is, unfortunately, from the wiki, and references a novel rather than a game so it's hard to say if it's
really canon or not, but it gives us a time limit of about a century before the Quarian people start to starve. At the same time, the second is Tali's quote, claiming that adapting to any environment other than Rannoch will take multiple centuries, a process that will likely only be exacerbated by their people starving
en masse in the meantime.
Presumably the time the Fleet tried to invade that one Council-claimed planet they must have discovered something that would make it conducive to being terraformed into a Rannoch-like state relatively quickly, otherwise they wouldn't have bothered. At the same time, they couldn't exactly tell the galaxy that their people are in danger of dying off, since most of the galaxy won't care, and might well try to hasten the process. So they get kicked off the planet by force of arms, and get labeled the villains of the piece, while the planet that could have saved their species (and probably marginalized the "Rannoch or die!" faction) became somebody else's colony instead.