http://www.ssa.gov/policy/docs/quickfacts/stat_snapshot/
Even if social security was completely removed for a basic income of 10k (I'll clarify again that I'm not endorsing that figure as a blanket basic income), it would be a cut of a couple thousand a year, not a cut of more than 10k as you claim. Hell you could even keep all the net SS+basic income payouts the same and social security costs would drop to 1/5th of what they are now, saving over a trillion dollars.
Also, That was like, one third of one fourth of my post. The fact that your estimate was way way off (far from "simple math") is barely changed by excluding social security.