In his last news conference before House members left Washington for a five-week summer break, Hakeem Jeffries, the Democratic leader, attacked Republicans for their signature tax cut legislation, accusing them of taking food and health care from poorer Americans to bolster the wealthy.

Then, he ceded the lectern to Representative Katherine Clark of Massachusetts, the No. 2 Democrat, who made a jarring pivot to a different topic.

“Instead of standing up for kids, for families, instead of standing on the side of transparency and accountability, Republicans are running away — all to avoid the release of the Epstein client list, all to cover up for pedophiles,” Ms. Clark said on Wednesday.

Shut out of power in Washington, Democrats have been searching all year for ways to throw a wrench in the works of Congress and gain the upper hand against a Republican majority that routinely bulldozes over them. They have focused relentlessly on making the economic case against President Trump’s agenda, bashing Republicans for backing policies they argue will hurt ordinary Americans.

But the deep G.O.P. fissure over the Trump administration’s refusal to release files on Jeffrey Epstein despite promises to do so has shaken that focus, giving Democrats an opening they have eagerly seized to gum up the works at the Capitol and stoke public anger about how Republicans are governing.

Over the past two weeks, Democrats have effectively paralyzed the House floor by insisting at every turn on forcing votes Republicans do not want to cast on whether to insist on the release of files related to Mr. Epstein, the financier who died by suicide while in federal custody on sex-trafficking charges.