The Democrats said they should be allowed to enforce their demands for Trump's financial records from his accounting firm immediately.
The House's plea to allow enforcement of its subpoena comes a few days after Chief Justice John Roberts imposed an indefinite delay to give the court time to figure out how to handle the case. Trump made an emergency appeal to the court to block the subpoena from being enforced in the meantime after an appeals court in Washington, DC, ruled against him.
A similar fight also has reached the high court from New York, where the Manhattan district attorney wants Trump's tax returns for a criminal investigation.
The justices probably will decide by mid-January whether to hear the New York case, and might want to deal with the two cases together.
Manhattan District Attorney Cyrus Vance Jr. said in a court filing Thursday that the justices should not get involved.
Trump has argued that presidents are immune from criminal investigation while they are in office. But Vance said earlier Supreme Court rulings forcing President Richard Nixon to turn over the Watergate tapes and allowing President Bill Clinton to be sued for sexual harassment demonstrate that Trump also should lose.
Unlike in those cases, Trump doesn't have to do anything since his tax returns are held by the Mazars USA accounting firm.
Trump's "main argument for review is that when the President seeks a writ of certiorari asserting immunity, this Court should grant it. But the petition provides no compelling basis for this Court's intervention here," Vance wrote.
Under an agreement with Trump's lawyers, Vance won't seek the tax returns until the court determines not to take up the case, or hears arguments and issues a final decision.
The case is on a schedule to be heard and decided by late June. The House wants a similar timeline for its subpoena fight, if the justices opt to hear the case.
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.