Suppose sequestration goes through with cuts of about 9.4 percent for defense spending and about 8.2 percent for non-defense spending. Under that scenario, AAAS project cuts in funding for non-defense R&D of 7.6-8.2 percent.
That's pretty bad, but it gets a lot worse if defense programs were protected from cuts. It's hard to know how much defense spending might be cut, but some have suggested that it be held sacrosanct. So AAAS examined what would happen if DoD didn't take any cuts at all. Then cuts in non-defense R&D were estimated at 10.4-17.5 percent.
The impacts would be devastating. I am most familiar with NSF, so I'll focus on the impact there. The FY 2012 appropriation was just over $7 billion dollars, so cuts of $1 billion per year amount to 1/7th of its budget. With success rates in programs I'm familiar with already less than 10 percent, NSF may have to eliminate some programs completely and drastically limit the size of awards that it makes. Neither would be consistent with its mission.
NSF is the only federal agency whose mission includes support for all fields of fundamental science and engineering, except for medical sciences. We are tasked with keeping the United States at the leading edge of discovery in areas from astronomy to geology to zoology. So, in addition to funding research in the traditional academic areas, the agency also supports "high-risk, high pay-off" ideas, novel collaborations and numerous projects that may seem like science fiction today, but which the public will take for granted tomorrow. And in every case, we ensure that research is fully integrated with education so that today's revolutionary work will also be training tomorrow's top scientists and engineers. (source)