Presidents from both parties have done their best to defy and limit Congress’s access to executive branch information in recent decades, but ultimately they have played by a set of unwritten rules that after leverage like subpoenas, budget appropriations and the possibility of public shaming have been deployed, the two sides meet somewhere in the middle.

Jason Chaffetz, Republican of Utah and the chairman of the House oversight panel during Barack Obama’s presidency, said Mr. Trump’s actions reflected an understanding that congressional subpoenas have been losing power for years.

“Your subpoena is only as good as your ability to enforce it,” Mr. Chaffetz said, “and the reality is the only way to enforce a subpoena is through the Department of Justice, so good luck with that.”

At least so far, Mr. Trump has chosen not to compromise with his Democratic investigators.

“He doesn’t care about any of that stuff,” Mr. O’Brien said. His Democratic critics, Mr. O’Brien said, “have no leverage over his conscience.”

Representative Maxine Waters, Democrat of California and the chairwoman of the House Financial Services Committee, told reporters on Tuesday that the latest lawsuit targeting her committee’s subpoena only highlighted questions about what in his financial history the president was so determined to hide from public view. Democrats, she said, would fight him “tooth and nail.”

“He may file the lawsuit,” Ms. Waters said, “but that is not the end of this game.”

Democrats are contemplating a range of responses. They could go to court themselves to try to seek orders enforcing the subpoenas. They could hold administration officials or other witnesses in contempt of Congress. Or they could initiate impeachment proceedings against Mr. Trump or other officials.

They appear determined to continue their financial investigations, as well. The House Intelligence Committee, one of the panels behind the subpoenas, has hired Patrick Fallon, the former head of the F.B.I.’s financial crimes unit, to aid the effort, according to a committee official who was not authorized to discuss it publicly.