“Those at the very top are shouldering less and less of their fair share of the tax burden,” Mr. Murphy said on Tuesday in a speech detailing his budget. “That’s the opposite of tax fairness. Let’s work together to apply the millionaire’s tax to every millionaire. By doing so, we can do more to relieve the burden on middle-class taxpayers and senior citizens who are taking it on the chin from the Trump administration’s tax scam.”

A Rutgers University poll just after Mr. Murphy’s election in 2017 found that nearly two-thirds of state residents favored a tax on those making over $1 million. But that was before the fallout from President Trump’s federal tax law hit the state, most significantly by limiting the deductibility of state and local taxes.

Only three states in the country, as well as Washington, D.C., have taxes that target those making more than $1 million: California, Connecticut and New York, which adopted a so-called millionaire’s tax during the recession a decade ago.

New York Mayor Bill de Blasio favors raising the tax, but Gov. Andrew M. Cuomo has said that it would have virtually no chance of passing in the Legislature.

Mr. Murphy had hoped to build on the momentum of his 14-point victory in 2017 and the Rutgers poll results when he called on raising taxes on the wealthy last year. But after opposition from Democratic legislators brought New Jersey to within hours of a government shutdown, a compromise was reached to raise taxes on those making over $5 million.

That tax raised $216 million last year, according to the state’s Department of Treasury. This year, Mr. Murphy said, expanding the tax to those making more than $1 million would bring in $447 million in new revenue, helping pay for priorities like improving New Jersey Transit, the state’s sputtering public transportation network, and paying down the state’s enormous public pension obligations.

But with the 80-member Assembly up for election this year, many Democratic lawmakers are wary of angering voters by pursuing yet another tax. Only a dozen or so applauded when Mr. Murphy mentioned the millionaire’s tax.