Getting in to a Top-Ten Political Science PhD: Low GRE, Excellent Rest?

<p>Hello all. Hopefully you have some good suggestions for me!
I just took the GRE and am a bit disappointed with my scores. Unfortunately, this is the second time I took the test and did even worse (substantially worse) the first time around. (I made the mistake then of not cancelling my scores even though I knew I messed up—big time.)
At the same time, I have a bit above a 3.9 GPA from what is often ranked among the top-five of universities, including an A average the three last years and A- average the first year, while undertaking an above average course-load.
I have some good post-college experience as well: I've worked at think tanks/ non-profit organizations in the U.S. and abroad (at the Research Assistant level), and undertook a one-year abroad scholarship. And I’m working on a publication (for a policy journal) to be co-authored with a well-known professor.
I have long thought about going into a PhD program in Political Science at a top-ten school, but am worried that the GRE will be the one thing that holds me back. In fact, fear of the GRE is a key reason that I have delayed applying to programs these past few years. I guess I’ve been lucky to have found other worthwhile opportunities, but I don’t want to delay my grad school applications any longer.
Does anyone really know how important is the GRE for a PhD at a top-ten school? Do they really sort applications by discarding those that don’t meet a certain GRE threshold?<br>
To clarify this time I got a 610 V, 730 M (estimate 85th percentile). The first time, a couple years ago, I got around the 50th percentile, perhaps a bit worse.
I know that I can take the GRE again, but how many times is acceptable? I am, moreover, concerned that I have some test-taking problems that might make it difficult for me to see a substantial improvement in my scores. They involve both issues of concentration and anxiety that tend to feed off each other. I get immensely psyched by the time pressure on the GRE. And this past time, I was actually supposed to take it a few days before I just did yesterday, but that morning I was so anxious that I became physically ill and was unable to get to the testing center. I was of course pretty ****ed about losing my money on that one and having to re-schedule for a few days later.
I won’t bore you with my self-reflection about these problems and why it is that they only affect me on standardized tests and not school tests (I’ve pretty much always been a straight-A student). And it is strange that I was able to get a decent score (98th percentile) on the SAT the second time I took it, but could never muster quite the same result on the ACT—whether on practice tests or the four actual times I took it (and I also bombed it the first time).
If someone has insight on my predicament from their own experience or from working in admissions, it would be much appreciated. Thanks.</p>

<p>Oops, I meant 620 V, not 610. Maybe this is just ok enough to get me in? Do I have to retake the GRE and do better? Anyone with relevant insight know?</p>