Sen. Lindsey Graham appeared to put himself in political jeopardy when he wrote and championed an overhaul of immigration laws, but he is poised to lap the field in Tuesday's Republican primary in South Carolina. GOP Sen. Lamar Alexander of Tennessee, who also backed the bill, is in a strong position ahead of his primary this August.

Rep. Renee Ellmers (R., N.C.) easily survived a primary challenge after backing liberalized laws. And Tim Donnelly, a leader in the movement to stop illegal immigration, lost to another Republican...