Hopefully not long. Unfortunately, I think the country will still "last" for quite a while, a decade at least, and possibly out past beyond our lifetimes. The United States has a huge amount of institutional inertia built up, overcoming that will take a long time and a lot of consistent fuckups hitting the population. I don't think it's guaranteed that there will be some kind of "collapse" at all. We've already taken several steps towards becoming a banana republic recently, I don't necessarily see that we won't simply end up fully becoming one. As Latin America continues to pour across the border the US might just slowly transition into a proper third world country during the rest of the 21st century.
If there is some kind of definitive "collapse" it will probably be due to an economic catastrophe of unprecedented proportions. Even the Great Depression didn't bring down the government, it just got FDR elected and social security implemented and etc. So an economic crisis big enough to cause a proper regime change would have to truly be "the big one" where the national debt bubble finally pops somehow. I won't pretend to have any idea how, when, or even if that will happen.