I was in the same situation really (GPA , a little higher GREs but doesn't matter, and state school). Play to your advantages in SoP, if they read it for more than 4 sentences, you got a good shot. 1) Have an interesting research question in SoP, 2) identify at least 2 faculty members you want to work for and why 3) tell them an interesting story at the beginning (use a narrative) that lead you to Poli Sci!
I did the same, got into some great top 15 programs; although I chose a top 20 program instead since a faculty member had ridiculously similar research interests.
Be confident, be smart, but more importantly - be excited. If you don't get it this time, then you have another amazing chance to wait it out and hone in on what you really want to do.