WASHINGTON—The Democratic-controlled House of Representatives is playing an unusually active role in federal courtrooms, where the fate of key Trump administration policies as well as the powers of Congress to investigate the president are at stake.

Douglas Letter, general counsel of the House, over the past two weeks has argued—and won—two cases involving congressional subpoenas seeking Trump financial records. That includes one Wednesday in which a New York federal judge announced his decision against the president at the end of a hearing; typically days or weeks pass before rulings are issued.

He also has argued two cases on the legality of President Trump’s plans to pay for a southern U.S. border wall without appropriations from Congress, including one Thursday in Washington, where the House sued the administration to block its plans.

“We’re going to do this as a traveling roadshow,” Mr. Letter joked last week during an Oakland, Calif., court hearing in which he argued that Mr. Trump “cannot build this wall without Congress.”

House Speaker Nancy Pelosi (D., Calif.), who hired Mr. Letter, said on Thursday that she believes it was Mr. Trump’s frustration with the court rulings this week on the subpoenas that led him to walk out of a Wednesday meeting on infrastructure with her and Senate Minority Leader Chuck Schumer. The president’s lawyers are appealing both rulings.