Throughout his 17-month campaign, Philip D. Murphy, the governor-elect of New Jersey and a Democrat, made promise after promise to voters: to fully fund the state’s floundering transportation network, fully fund its underfunded schools and to fully fund the underfunded public pension system, all part of a far-reaching progressive agenda that led to a 14-point victory in last month’s election.

Essential to Mr. Murphy’s agenda was a so-called “millionaire’s tax’’ to be levied on the state’s wealthiest residents. After the election, Mr. Murphy and his allies in the Democratic-controlled State Legislature made passing the tax their top priority when he takes office in January.

But now the federal tax bill passed by the Senate, which takes aim at high-tax and Democratic-leaning states like New Jersey, is threatening both House Republicans from New Jersey, who will be pressed to vote on a measure that will harm their constituents, as well as the state’s Democratic agenda.

While Mr. Murphy has remained adamant that state lawmakers press ahead on the tax on the wealthy, Stephen M. Sweeney, the State Senate president, and Craig Coughlin, the incoming Assembly speaker, have both said that they want to reassess the wisdom of pursuing a new tax when so many residents are facing the prospect of far higher tax bills.