Graham has reached out to the Tea Party movement in the Palmetto State this week and appeared on conservative radio in a bid to explain his record to right-leaning voters.

Some grassroots conservatives are frustrated with Graham for partnering too often with President Obama and congressional Democrats. Graham was the lead Senate GOP negotiator on climate change and immigration legislation, though neither package moved forward in the Senate.

Graham met with the Tea Party group in Charleston, S.C., on Wednesday in a closed-door meeting. The Charleston County Republican Party has been among several county chapters and Tea Party groups to censure Graham, citing concerns about the second-term senator's stances on immigration, Supreme Court nominees and energy and climate legislation, among other issues.

The Tea Party appearance was paired with appearances on conservative radio in the state, where Graham faced tough questions about whether he was adequately conservative.

Graham defended himself as a mainstream conservative, and expressed worry that public officials like himself were being effectively prohibited from expressing disagreement with the party.

"If you can't accept me pushing back, then our party does have a problem. It's OK for you to push back against me, but it's OK for me to push back against you," Graham said on WTMA radio in South Carolina, where he received a grilling over his record. "You may not like my political style of trying to find compromise on the big issues of our time, but I think it's the heart and soul of what makes America great."

He touted his decision to endorse ending birthright citizenship for the children of illegal immigrants in highlighting his conservative bona fides, though he couched it as part of a broader effort to win support for comprehensive immigration reform. He denied the move was meant to shore up support among South Carolina conservatives.

"What I'm trying to do is make a comprehensive approach more attractive to more people," he said.

Though Graham was reelected in 2008, he's no doubt cognizant of the difficulties many of his Republican Senate colleagues have faced this cycle.

Two senior Republican senators — Lisa MurkowskiLisa Ann MurkowskiMcConnell names Senate GOP tax conferees Week ahead: Trump expected to shrink two national monuments GOP on verge of opening Arctic refuge to drilling MORE of Alaska and Bob Bennett of Utah — were defeated by conservative challengers in primary contests, and Arizona GOP Sen. John McCainJohn Sidney McCainGOP strategist donates to Alabama Democrat Meghan McCain knocks Bannon: 'Who the hell are you' to criticize Romney? Dems demand Tillerson end State hiring freeze, consult with Congress MORE, a close ally of Graham's, moved to the right to defeat a primary challenger.

In South Carolina, three-term GOP Rep. Bob Inglis earlier this year lost his primary battle 71-29 to conservative Trey GowdyHarold (Trey) Watson GowdyTop intel Dem: Trump Jr. refused to answer questions about Trump Tower discussions with father Overnight Cybersecurity: Panel pushes agencies on dropping Kaspersky software | NC county won't pay ransom to hackers | Lawmakers sound alarm over ISIS 'cyber caliphate' Flynn told associate Russia sanctions would be ‘ripped up’ early in Trump presidency MORE in a runoff.

(Graham won reelection 58-42 percent in 2008, a Democratic wave year, against Democrat Bob Conley.)

Graham won't be up for reelection until 2014, but conservative activists' anger toward him suggests he'll face a primary challenge in four years. He said that he'll keep pressing forward toward consensus.

"I'm not a Barry Goldwater Republican; I'm a Ronald Reagan Republican," he said. "If this country's going to survive, we've got to work together in a common-sense way."