Sen. Lindsey Graham (R-S.C.) said Mitt Romney needs to win a southern state on Super Tuesday to end the GOP primary, and that a win in Ohio wouldn't be enough to force his opponents out of the race.

"Ohio is not the only state — if he wins in Ohio that'd be good for the narrative that [the primary] needs to end, but you have to look at Tennessee too, it's not just Ohio... If you win Ohio and Tennessee then you've got a pretty good narrative going," Graham told The Hill Tuesday afternoon. "He needs to perform in places where people thought he would not do well." 

Romney lost badly in South Carolina and while he won Florida's primary that state is culturally different from the rest of the South. He has struggled with Tea Party supporters, very conservative voters and Evangelical Christians, three groups that have large sway over GOP primaries in many southern states.

Graham said that a win in Oklahoma would do the same thing for Romney as one in Tennessee, but that Romney's opponents would have plenty of reason to keep running if if he doesn't.

"If he has a good Super Tuesday there'll be momentum to bring this thing to a conclusion," he said. "If it's a mixed decision, it goes on."

Graham has not endorsed any of the Republican candidates.