Texas Republican Rep. Ron Paul took to the cable networks today to jab back at South Carolina Republican Sen. Lindsey Graham, who over the weekend said he would not sit back and watch the Texan “hijack” the GOP with his brand of Republicanism.

“My first reaction would be, ‘What does he have against the Constitution?’ And the supporters I have support me because I’m a traditional conservative and I support the Constitution,” Paul told CNN in an interview tonight.

He cited Graham’s support of TARP funds and the wars in Iraq and Afghanistan and “all the big government things” as examples of why his supporters feel lukewarm about the GOP. “These are the things that constitutional conservatives don’t support,” he said.

The spat was sparked during a contentious Oct. 12 town hall meeting in Greenville, S.C., when Graham engaged in verbal combat with constituents who questioned his GOP credentials and urged him to be a little more like Paul. (Click here to watch the video.)

“I’m going to grow this party. I’m not going to let it be hijacked by Ron Paul,” Graham said to jeers. One heckler called out: “You’re the one that hijacked it!”

Another constituent questioned the senator’s adherence to constitutional principles, and aligned herself with the Constitution Party “because I’m a constitutionalist, senator, and you are not.” In his reply, Graham said that “Ron Paul’s run for president like 39 times. He keeps losing.”

Graham argued that if the GOP only caters to one wing of the party they will become a permanent minority. “If you want 30 pure Republicans who think exactly like you, [Senate Majority Leader] Harry Reid would say ‘Send them on’… he’ll run right over us. And this country that we know, you’re going to turn over to the most liberal people in the world because you can’t believe someone disagrees with you.”

Their war of words is emblematic of larger battles brewing within the Republican Party over how best to heal the electoral wounds suffered in 2006 and 2008, rebrand itself, and build a new generation of party leaders.

Paul adheres to a strict political philosophy on economic and foreign policy that’s helped him carve out a role as party outsider. It also allowed him to build a small but fierce political following during the presidential campaign that tapped in to voter anger on issues ranging from the war in Iraq to the Wall Street meltdown.

Graham, a deal-maker who has worked to build consensus on key issues, is a political ally and personal friend of Paul’s 2008 presidential primary opponent, Arizona Sen. John McCain. He said he wants to rebuild a “big tent” GOP.

Asked if he felt he represents the current GOP more than Graham, Paul said, “Probably not.”

But he added, “I’ll tell you what, I’ll bet you the vote would come out a lot closer right now if you compared the supporters of Lindsey Graham and Ron Paul than it was two or three years ago.”