By any definition, South Carolina Senator Lindsay Graham is a conservative. Yes, he voted to confirm President Obama’s nominees for the Supreme Court and has voiced support for climate change legislation and higher taxes, but those are small deviations.

On almost everything else, Graham sides with the right flank of the GOP. He supported Paul Ryan’s budget and its variations, touted the “Cut, Cap, and Balance” plan — which calls for huge reductions in federal spending — and has been a vocal critic of the Obama administration on national security issues, including the ongoing controversy over the attack in Benghazi.

But for right-wing activists in South Carolina, Graham’s credentials still aren’t conservative enough. Politico reports that there’s a solid chance he’ll face a challenge from the right. It’s not just because of the issues, however. As Jonathan Martin writes: “What so irritates his conservative critics is not just his issue positions but the way he’s unapologetically pragmatic about politics in a way that’s gone out of fashion on GOP circles.”

That’s just another way to say that Graham’s critics are as upset with his willingness to compromise and legislate — even if it advances conservative priorities — as they are with his votes. The mere fact that Graham occasionally works with Democrats to accomplish something is enough to earn him opposition from the base of the Republican Party.

When observers like Jonathan Bernstein say that the Republican Party is “broken,” this is what they mean. The structure of our government doesn’t require comity or non-ideological political parties; after all, ideological polarization doesn’t preclude compromise.

The only thing it requires is a willingness to work together. Just because your end goal is a dramatically smaller government doesn’t mean you can’t cut a compromise to slightly advance the ball, or make movement on an issue unrelated to that priority.

But as it stands, a key portion of the Republican Party is opposed to any form of compromise, even ones that would result in conservative victories. More importantly, they’re willing to take action against politicians that violate this new commandment and work with Democrats.

Under those conditions, gridlock is inevitable, as GOP politicians constantly work to avoid a primary challenge, funded by outside donors. In the absence of institutional change — ending or reforming the filibuster, for example — there’s not much you can do to get around this dynamic. And to alter it, you need figures in the Republican Party that can stand against the base. So far, few have been willing to take that step.

If right-wing opposition to Lindsay Graham’s reelection bid shows anything, it’s that the core problem in American politics right now is the dysfunction of the Republican Party.

Jamelle Bouie is a staff writer at The American Prospect, where he writes a blog.