Representative Lloyd Doggett, the Texas Democrat who questioned Mr. Mnuchin on the tax issue, found the response to be unpersuasive.

“What he said today was little more than mumble jumble double talk,” Mr. Doggett said after the hearing.

The Ways and Means chairman, Representative Richard E. Neal of Massachusetts, says his staff is working closely with the House general counsel, Doug Letter, to prepare documentation to make a request in the coming weeks. But as Democrats anticipate a legal challenge from the Treasury Department, he has been exceedingly tight-lipped about even his most basic plans.

Democrats argue that the law’s intent does, in fact, support requesting the president’s tax information, and held a hearing last month in part to bolster that interpretation. The provision in question, they point out, was born out of the Teapot Dome scandal of Warren G. Harding’s administration and aided another congressional committee in an investigation of President Richard M. Nixon’s tax positions in the 1970s.

Though the law does not require the chairman produce a rationale for a given request, Democrats believe it will help bolster their case in an eventual legal fight. In addition to the public hearing, Mr. Neal has asked other House committees to give him their own reasoning for why the documents are relevant to Congress’s work.

But the deliberative approach taken by Mr. Neal, a veteran Democrat who prefers striking legislative deals to the flash of oversight battles, has drawn the ire of liberal activists and some members of his own caucus who do not understand why he has not yet filed a request. They have tried to push Mr. Neal toward making a longer list of demands and to do so quickly — though their effect is uncertain.

Mr. Neal has repeatedly declined to answer key questions about what he will seek, including how many years worth of Trump returns he will request and whether he will try to obtain tax information on Mr. Trump’s myriad businesses.