Democrats on the House and Senate tax-writing panels have found some places where they agree with the Treasury secretary, despite spending months berating the administration for what they view as unfair tax changes.

Treasury Secretary Steven Mnuchin appeared before both committees on March 14, in planned hearings on the latest White House budget proposal. The meetings weren’t without their awkward moments: Mnuchin, for example, demurred when asked whether he would comply if Democrats request President Donald Trump’s tax returns, saying he will consult with lawyers and “follow the law.”

Still, Democrats will need bipartisan support and administration buy-in to...