Sen. Lindsey Graham (R-S.C.) urged House Republicans to accept a "fiscal cliff" deal passed by the Senate early Tuesday morning -- and to prepare to extract concessions from Democrats in exchange for raising the debt ceiling. 

If the House fails to pass the deal, Graham told Fox News, "We're going to get blamed and about two weeks into this, we'll fold like a cheap suit." Instead, he urged Republicans, “Work with me and others never to raise the debt ceiling again unless we address why we’re in so much debt."

Graham made a similar comment to the National Review, saying, "It’s not all I would have liked, but it’s called American democracy, so on to the debt ceiling."

And on Twitter, he wrote, "The debt ceiling fight is where we can make major spending changes and prevent the country from becoming Greece."

Graham is up for reelection in 2014, and he could face a tough primary challenge from the right. He's clearly seeking to make the case to conservatives that Tuesday morning's vote doesn't mean caving on spending.