I applied last year with a 710 Quant score on the GRE, and two math-y classes, a political science methods course and an upper level statistics course (did not get an A). Among the top programs I got into were Berkeley, UCSD, and Michigan. The rest of my application package was pretty good, but nothing super exceptional. In my experience, then, strong math skills are not a prerequisite to entry into top programs.
That being said, my life would be much easier if I knew more math. Not only would the methods classes that I want to take be less work (I've had to teach myself calculus in a very short time frame, and that is a tough task, and I still find proofs impossible), but I'd be able to take far better advantage of the many math tools available.