As long as South Carolina gets to vote yea or nay on whether he stays or goes, it will never happen. They will always vote yea, even if they have to exhume from the cemetary.
He’s very much at risk in the primary. He has lucked out twice, first in 2008 when the Bush White House interfered to knock out his first tier challenger (Thomas Ravenel) with conveniently made federal drug charges, and in 2014 when 6 second-tier challengers stepped up and divided the field so badly that no one was able to gain traction.
If Graham were to face any of the sitting House members or any of the statewide elected officials one-on-one, he would lose outright. At least 10% of the voting electorate simply won’t vote for him in the general election, why he underperforms. He should be, as a Republican, getting well over 60% of the vote, as high as 65%, but he registered his lowest % in 2014, barely over 54%, a fraction below his first race in 2002 when he was more highly regarded by the Conservative base as a House Impeachment Manager against Clinton.
Look at his Senate seatmate, Tim Scott, who has scored 61% in both the 2014 special and 2016 general elections, outstripping Graham by 7% in that 2014 election when they were both on the ballot. He scored 90% in the 2014 GOP Senate primary and went unopposed in 2016. If Graham wasn’t such a creepy weasel and left-wing ass kisser, this is how he’d be performing.