LAKE WYLIE, S.C. — Some of the early shots in the Republican primary battle against Senator Lindsey Graham have been fired from this tiny community on the northern border of the state where the Civil War began.

A small group called Carolina Conservatives United, one of dozens organized loosely under the flag of limited government, low taxes and strict adherence to the Constitution, sent out images last week of a milk carton bearing Mr. Graham’s face and asked Gov. Nikki R. Haley to issue the state’s version of an Amber Alert to find its missing senator.

“Lindsey Graham has not been seen in the state of South Carolina for most of the last two years,” said Bruce Carroll, the chairman of the group.

Conservatives in South Carolina are eager to oust Mr. Graham, who has enraged the far right for, among other things, reaching across the aisle on immigration and supporting President Obama’s nominations for the Supreme Court. Tea Party supporters called him a community organizer for the Muslim Brotherhood when, instead of heading home for the Congressional break this month, he went to Egypt at the request of the president.