Graham: Trey Gowdy for the Supreme Court

Sen. Lindsey Graham is contemplating a 2016 presidential bid.

Washington (CNN)Sen. Lindsey Graham's plan to convince conservatives he's with them on immigration starts with nominating Rep. Trey Gowdy for the Supreme Court.

As the South Carolina Republican moves toward a 2016 presidential run, he said Sunday on CBS's "Face the Nation" that he'd tap his fellow Palmetto State lawmaker -- a leading critic of President Barack Obama's immigration actions -- for the high court.
He said he'd expect Gowdy to win confirmation because "he's a qualified person."
    His pitch for Gowdy came as Graham was asked about his views on immigration reform -- which have sometimes angered conservatives, leading them to label his stance "Lindsey Grahamnesty."
    "Paying illegal immigrants under the table is a real threat to middle-class wage growth," Graham said. "That's one of the reasons we need to fix immigration. But my view on immigration is shared by 70% of the American people."
    As he made those comments, Graham pivoted toward his most comfortable topic: national security.
    "I'm very comfortable that I'm in the mainstream of conservatism. I've done very well in a red state, and when it comes to national security and understanding the threats our nation faces, I believe I'm the best qualified of anybody on our side of the aisle to offer an alternative to a failed foreign policy of Barack Obama," Graham said. "We'll never have peace with a radical Islam, but we can have security."
    Graham also talked foreign policy on Sunday, saying the United States needs to put 10,000 "boots on the ground" to combat ISIS in Iraq and Syria.
    "There's got to be some regional force formed with an American component -- somewhere around 10,000, I think, American soldiers -- to ally with Arab armies in the region and go into Syria and take that territory from ISIL," Graham said, using another name for ISIS.