“Congress in effect placed tax return information in a locked safe in 1976, but it preserved one key for purposes of disclosing such information to the public,” said George K. Yin, a University of Virginia tax law professor. “It gave that key to the tax committees. The law therefore should be interpreted to enable the tax committees to use the key in appropriate and necessary circumstances.”

Only one of the panelists, Ken Kies, a former Ways and Means aide and veteran Republican tax lobbyist, disagreed.

The committee’s chairman, Representative Richard E. Neal of Massachusetts, is working closely with the House’s general counsel, Doug Letter, to build a legal rationale that could withstand a court challenge. Mr. Neal, who prides himself more on his bipartisan policymaking skills than hard-nosed partisan oversight, is reluctant to move too quickly and risk making a mistake that could be exploited in court, people familiar with his thinking said.

Though it focused almost exclusively on invoking existing authorities, for instance, Thursday’s subcommittee hearing was technically a legislative session concentrated on a portion of Democrats’ broad election reform bill that would require all presidents and vice presidents to disclose their tax returns going forward.

But pressure from Mr. Neal’s left flank is growing. Three liberal groups — Tax March, Stand Up America and Indivisible — recently wrote a letter urging the chairman to “stop slow-walking” and even attached another form letter, addressed to the Treasury secretary and the Internal Revenue Service commissioner, for Mr. Neal to sign formally requesting the returns. Liberal lawmakers, too, are growing impatient.

Mr. Neal has not indicated when he plans to make a formal request under the law, how he would review what he got or if his committee or others will convene additional hearings first. Nor has he said whether he will request tax information on the Trump Organization or just the president’s personal returns.

As written, the law does not give the Trump administration clear grounds to deny a request from Mr. Neal. It says only that the Treasury secretary “shall” furnish the information upon request.