Graham scored a victory last week when U.N. Ambassador Susan Rice withdrew her name from consideration as a candidate for secretary of state. The senator had been one of her most outspoken critics.

“A feather in Sen. Graham’s hat,” said one Capitol Hill lobbyist. “He stood up, put up a principled fight … and now his position has been validated. This will register with GOP voters in the South. It was a smart fight to pick, and he won.”

Some say Graham’s media-savvy, deal-cutting approach to politics should serve as a model for national Republicans as they try to rebrand the party after its November thumping at the polls.

Graham, a two-term senator and former congressman, “has crossover appeal. He knows how to message and appeal to Democratic voters, even African-American voters,” said Glenn McCall, a Republican National Committeeman in South Carolina who served on Mitt Romney’s Black Leadership Council.