State Sen. Donna Campbell likes to tell gatherings she’s the most conservative person in the room. She’s of the sort who taunts Democrats for being soft and out of touch with “real” Texas values and likes to take aim at hot-button issues like gun control.

Now comes her challenger in this November’s election, Steve Kling, a Democrat who also happens to be a combat veteran and the former commander of an Army Reserve small-arms fire team. Campbell’s been trying t...