WASHINGTON — Senator Lindsey Graham, Republican of South Carolina, ought to be a prime target for a Tea Party challenge. He helped write the Senate overhaul of immigration laws that provided for a pathway to citizenship for illegal immigrants, backed President Obama’s Supreme Court nominees and expressed a willingness to raise taxes as part of a larger deal to address the nation’s fiscal health — all perilous positions in a deeply conservative state.

Yet none of the six Republicans in South Carolina’s House delegation or any statewide elected officials moved to take on Mr. Graham. So as his June primary approaches, he is using some of his $7.5 million in campaign funds to fill television screens in the state with ads as he faces a field of relative no-names.

Mr. Graham’s unexpectedly strong standing underscores a larger point: The Tea Party may be nudging Republicans to the right in Congress with the implicit threat of primary challenges, but when it comes to recruiting quality challengers to take out incumbent senators, it is falling decidedly short.

“I think Republicans are really focused on winning back the majority and people can now see 51,” Mr. Graham said of the Senate.