OMAHA, Neb.—Rep. Don Bacon was sitting in church on a recent Sunday when the freshman Republican stole a look at Facebook on his iPhone. He was surprised to see a super PAC advertisement for his own re-election—which is still 20 months away.

To try to preserve control of the House in the face of anticipated stiff headwinds, Republican operatives are starting 2018 congressional campaigns earlier than ever before.

The...