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 GrahamProgressives rave over Harrison's start at DNC Senate confirms Garland's successor to appeals court Progressives want to tighten screws beyond Manchin and Sinema 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 PaulRand Paul does not support a national minimum wage increase — and it's important to understand why Fauci to Chelsea Clinton: The 'phenomenal amount of hostility' I face is 'astounding' GOP's attacks on Fauci at center of pandemic message 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.