Odds of Getting In
Here's the thing: There are more people trained as political scientists than you can shake a stick at…but there just aren't that many jobs for political scientists. Does this suck? Yes. Does this mean you should toss aside your dreams of Capitol Hill and become a Starbucks barista instead? Of course not.
If you want to make it as a political scientist, you'll have to enter your post-grad school job search having already set yourself apart from the pack. How do you do that? Maybe you've volunteered extensively with local, state, and/or national political campaigns over the years. Maybe you interned with a local, state, or federal office holder for a semester or three. Maybe you wrote a policy memo or academic paper that was published by a reputable journal.
The point is, while a graduate degree in political science is a beautiful thing, it's just one of the items you'll need to land a gig as a practicing political scientist.