ROWLAND HEIGHTS, Calif.—Nowhere does the House GOP face a tougher task holding seats in November’s midterm elections than in the eight districts where Hillary Clinton won in 2016 and the incumbent is retiring—putting the pressure on Republican nominees such as Young Kim to win in Southern California.

“Those districts are like ticking time bombs. The incumbent has held them on borrowed time as the district has shifted away,” said David Wasserman, House editor of the nonpartisan Cook Political Report. He added that since 1992,...