I don't have hard numbers on this, but dramatic reductions in tax rates usually lead to dramatic improvement in the economy, which in turn leads to more gross revenue for the government even with a smaller percentage. Worked that way when Reagan did it, and also with the JFK tax cut IIRC.
In which case, 10% might be enough...especially since, if we stop being the Global Police, we could put half our active-duty troops into the Reserves and still be extremely secure against invasion. (IMO)
You'd have to do away with all entitlments, and all Federal programs that essentially equal "robbing Peter to pay Paul", of course. That's where the bloat in the budget really is.
Of course, the gov't is about as likely to do all that as a pig is to grow wings and fly. In fact I'd have to bet on the pig.