WASHINGTON — The high costs of health care are a driving force animating House Democrats in the swing districts that will decide control of Congress next year, with the electoral consequences of their votes to impeach President Trump unclear and a court ruling that left the fate of the Affordable Care Act in limbo.

From the suburbs of Seattle, Chicago, Philadelphia and Richmond, Va., to East Lansing, Mich., and Southern California, first-term Democrats see the worries about health care that secured their 2018 elections playing out again in 2020, and they are eager to run toward them.

“I have done 15 town halls in my district this year and the top issue I have talked about is lowering prescription drug costs,” said Representative Andy Kim, Democrat of New Jersey, who has made addressing health care costs the central point of his legislative agenda and his re-election campaign. “The cost side of things is something people see on a daily basis. It’s something tangible that they understand is a problem.”

The House majority in 2020 will be decided in roughly two dozen districts like Mr. Kim’s in south central New Jersey, where Republican voters outnumber Democrats, but where a Democrat nonetheless picked off a Republican incumbent in 2018. Democrats hope the debate over rising health care costs will give them a decisive advantage, especially in suburban districts where Mr. Trump, who has failed to deliver on his promises to lower drug prices, remains unpopular.