Yin told CNBC that a request to get Trump's tax returns would likely be consistent with the committee's oversight role and its ability to investigate. In a 2017 op-ed Yin said the tax committees had a right under the law to order a public tax return disclosure "as long as a disclosure served a legitimate committee purpose."
Both sides of the issue appear to anticipate a fight if the written request is sent.
House Speaker-designate Nancy Pelosi, D-Calif., said in December that obtaining the president's returns is "a little more challenging than you might think."
"I'm sure that the White House will resist, and the question is, where do we go from there?" Pelosi said.
NBC News reported Wednesday that House Democrats have added a provision to a forthcoming bill that would require presidential nominees to disclose a decade of tax returns shortly after being nominated. That bill would affect future candidates, but not Trump.
Some of Trump's defenders have decried prior attempts to snag Trump's tax filings as politically motivated.
Former N.J. Gov. Chris Christie, a Republican, in May 2017 vetoed a bill that would have required Trump to show his taxes if he ran for re-election in the state. The bill represented "politics at its worst," Christie said at the time.
Trump's lawyer, former New York Mayor Rudy Giuliani, said in the AP story that Democrats may have trouble proving that their demand is a legitimate legislative move, rather than a partisan maneuver.
Kamin told CNBC that it's possible Mnuchin could refuse to comply with the request, perhaps by arguing that Congress is exceeding its constitutional authority. But Mnuchin, who would be a central player in the process Democrats are expected to utilize, has merely reiterated through a representative that he "will review any request with the Treasury general counsel for legality."
IRS Commissioner Charles Rettig could also technically refuse to comply with Mnuchin's direction to collect Trump's tax returns. Prior to joining the Trump administration, Rettig had defended Trump's refusal to release his filings.
"Would any experienced tax lawyer representing Trump in an IRS audit advise him to publicly release his tax returns during the audit? Absolutely not," Rettig wrote in an op-ed in 2016 when he was a partner at accounting firm Hochman, Salkin, Rettig, Toscher & Perez.
Still, Kamin said he believes Democrats could prevail even in the face of a legal challenge.
"If they root this in the proper investigation and oversight," Kamin said of the committee Democrats, "they should get it."