Cash, a social conservative activist who narrowly lost a House primary runoff election to now-Rep. Jeff Duncan (R-S.C.) in 2010, said Graham has lost touch with South Carolina values.

"I am running to replace Senator Lindsey GrahamLindsey Olin GrahamBiden: Trump attending inauguration is 'of consequence' to the country The Memo: Harris moves signal broad role as VP Former US attorney asks for probe of allegations Graham pressured Georgia official MORE because I believe that after 20 years in Washington he is out of touch with South Carolina values and voters. Although Senator Graham might be hard-working and sincere, I cannot distinguish his core principles and can no longer trust his judgment," he said on his website.

"It is time for a new voice in Washington. We need a voice that represents Christian, conservative, and Republican principles instead of the latest bi-partisan 'deal' that simply makes matters worse."

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Cash said "the origins and foundation of American greatness lies in Christianity, Capitalism, and the Constitution" and promised he was "unapologetically committed to faith and family as the essential elements of enduring freedom."

Polling shows Graham is in a fairly strong position for reelection. But some on the right are unhappy about his bipartisan work on a number of issues, such as immigration reform. Libertarians in the party don't like Graham's foreign policy views and are still furious about his attacks on Sen. Rand PaulRandal (Rand) Howard PaulOvernight Defense: Lawmakers release compromise defense bill in defiance of Trump veto threat | Senate voting next week on blocking UAE arms sale | Report faults lack of training, 'chronic fatigue' in military plane crashes Senate to vote next week on blocking Trump's UAE arms sale McConnell in tough position as House eyes earmark return MORE (R) following the Kentucky senator's talking filibuster of President Obama's CIA director nominee, John Brennan.

Other Republicans are mulling a challenge to Graham as well, including state Sen. Lee Bright (R) and Paul backer Nancy Mace.