COLUMBIA, S.C. - A day after soundly defeating six Republican challengers, U.S. Sen. Lindsey Graham says he will try to push the GOP to solve hard problems like immigration.

Graham said Wednesday it would be a mistake to scuttle reform efforts after the stunning upset of House Majority Leader Eric Cantor in Virginia. Cantor's little-known tea-party challenger won by double digits over the single issue of immigration.

Graham says as long as the nation's borders are broken, the issue cannot be dead, and if it is, that's a sad day for America. He says lawmakers must fix immigration.

Graham has been criticized for working with Democrats on the issue. But he says the primary shows voters believe he can be conservative while at least trying to solve problems.