When I run my retirement scenarios, I do plan for SS being there. However I also run another set of numbers, assuming no SS whatsoever, just to see how much of an impact there would be.
And surprisingly, not that much. In most instances, it does significantly affect my chances of retiring in any given target year. For instance, according to Firecalc, I could retire this year, with a withdrawal of $80K per year, and have a 93.9% chance of success. Assuming no SS, that would drop to 78.8%. I'm shooting for a 95% chance of success, although 93.9% would get me close enough to be comfortable, if I was truly ready to retire.
If there was no SS at all, I'd have to cut back to $70K per year, if I wanted a 93.9% chance of success. Or, if I wanted to work a bit longer, and really wanted that $80K, then next year, I'd have an 84.8% chance of success, and if I pushed it out another two years, 92.9%.
In most instances, if I want the same $ amount, the No-SS scenario has me working another 2-3 years. Or, if I want to go out the same year, it drops my chance of success around 13-16%.
As for my tolerance threshold, 95% or greater means I'd be comfortable doing it. 80-95%, it would just depend, on my mood at the time, circumstances, the economy, etc. And, how close to 95%, or 80%, I am. However, I wouldn't retire with a less than 80% chance of success, unless really forced to.
However, everybody's circumstances will be different. In my case, SS isn't a huge percentage of my my annual draw, to begin with. For instance, if I was to retire this year...well, I'm 50 now. Won't get SS until 62, and the estimated benefit will only be about $16K per year. So right now, I have a 93.9% chance of making it for 12 years, relying solely on my investments for that $80K, and then at 62, SS is only accounting for about 20% of my annual budget.
For someone more dependent on SS, obviously a cut will hurt them more than me. However, I'm sure it will still be there, in some form, for the foreseeable future. And any alterations they make, won't hurt things as much as my worst-case scenario of it going away entirely!