WASHINGTON — President Trump’s administration foreshadowed weeks, if not months, of trench warfare with Congress on Tuesday as it defied demands for documents and testimony on multiple fronts in an effort to thwart expanding investigations mounted by House Democrats.

While Democrats debated the merits of pursuing impeachment against Mr. Trump, his advisers signaled that the administration would resist efforts to obtain the president’s tax returns and force his former aides to testify. The refusals could lead to constitutional clashes in court as Mr. Trump seeks to stave off further inquiries into his personal and political matters.

White House lawyers indicated that they planned to tell Donald F. McGahn II, the former White House counsel, and other former officials not to comply with subpoenas for their testimony, according to a person familiar with the legal strategy. The White House also blocked a former official from answering questions about security clearances to officials including Jared Kushner. And the Treasury Department refused to turn over Mr. Trump’s tax returns before a deadline set by House Democrats.

“I agree with the strategy of now fighting everything, the way Clinton did initially,” said Rudolph W. Giuliani, Mr. Trump’s personal lawyer, referring to President Bill Clinton’s approach to investigations in the 1990s. “We already gave every document we have, every witness we have. I don’t think the White House should sit by and have them do it all over again.”