As the midterm election season began, Republicans said they weren’t quite sure what to do with President Trump. His approval rating in January was 39% in The Wall Street Journal/NBC poll, and several special elections offered mixed evidence about the wisdom of embracing him.

His favorability rating has since risen, and with dozens of toss-up House and Senate races, Republicans’ need to energize Mr. Trump’s core supporters has turned him into the party’s political closer.

He has held 20 campaign rallies across the country since Labor Day, with another one Thursday night in Columbia, Mo., and nine more planned for the final five days. Mr. Trump is named in about 16% of all House and Senate ads, a recent Wall Street Journal analysis found, more than any other topic except health care and taxes. As he declared at an Oct. 2 rally in Mississippi, “I’m not on the ballot. But in a certain way, I am on the ballot.”

Steven Law, president of the Senate Leadership Fund, a super PAC aligned with Majority Leader Mitch McConnell (R., Ky.), said the 2018 midterm is already a referendum on the president, so the party should embrace the momentum he might be able to deliver. “With a president as colorful and engaged and omnipresent as this one, you take that natural historical dynamic and put it on steroids,” he said.

Mr. Trump is focusing mostly on Senate and governor races, his political aides say, and that tactic shows up in his travel. Only 10 of his rallies have taken place in House districts that the nonpartisan Cook Political Report calls either toss-ups or leaning slightly one way. The House midterm battle is mostly in suburban seats, where Mr. Trump is less popular, polls show.