WASHINGTON -- The stage is set for what could be a major battle between Gov. Phil Murphy and the state's top two lawmakers over whether New Jersey will raise taxes on millionaires.

Both state Senate President Stephen Sweeney and state Assembly Speaker Craig Coughlin have signaled they're not on board as Murphy, a fellow Democrat, renews his call for a millionaires tax.

During a speech Thursday night in Washington, D.C., Murphy doubled down on the promise he made during last year's campaign to institute the tax to increase spending on education, transportation, and public-worker pensions in the Garden State. The governor hinted the tax will be included when he unveils his first state budget March 13.

But Sweeney, D-Gloucester, has repeatedly said in recent months the state can't afford any tax hike in the wake of the federal Republican-sponsored tax law, warning that wealthy residents would flee.

And the morning after Murphy's speech, Sweeney said in a phone call with NJ Advance Media on Friday that he hasn't budged and still sees a millionaires tax as only a "last resort."

Sweeney declined further comment.

At the same time, Coughlin -- the state's second-most powerful lawmaker -- showed he's also leery of the idea.

"Our top priority should be to reduce spending, better manage our existing resources, and fully examine all revenues from existing programs before we raise taxes on anyone," Coughlin, D-Middlesex, said in a statement to NJ Advance Media on Friday.

Murphy needs both the Senate and Assembly -- the two chambers of the state Legislature -- to pass a millionaires tax before he can sign it into law.

The Democrat-controlled Legislature passed a millionaires tax multiple times in recent years, only to see then-Gov. Chris Christie, a Republican, veto it each time. Now, with Murphy as governor, Democrats run all branches of state government.

But the clash between Murphy and the two legislative leaders could lead to uncertainty over the budget in the months before the June 30 deadline for it to be signed.

Without a millionaires tax, Murphy would have to find revenue elsewhere to pay for his priorities or cut government spending.

Complicating matters is that Murphy and Sweeney have had a rocky relationship in the six weeks since Murphy was sworn in to succeed Christie.

Still, another top Democrat said there's no reason for alarm, at least not yet.

"I'm not nervous at this point," state Senate Majority Leader Loretta Weinberg said Friday.

"We have to come to an agreement," Weinberg added. "We have got to have a meeting of the minds."

Weinberg said she's always supported a "true millionaires tax" -- meaning only households who earn more than $1 million will see their income taxes rise.

"It's not only about balancing a budget," she said. "We also need more revenue for obvious reasons."

Murphy said Thursday that "only through tax fairness can we once again be a state that delivers more and invest in the things that benefits businesses and families."

"We cannot wait," the governor added.

Murphy added that the tax hike may be temporary. He said he'd be prepared to "recalibrate and reconsider" the increase if there's economic growth.

The uncertainty over the hike comes only eight months after a budget dispute between Christie and then-Assembly Speaker Vincent Prieto, D-Hudson, caused a three-day state government shutdown.

And the last time Democrats controlled state government, a budget battle between then-Gov. Jon Corzine and then-Assembly Speaker Joe Roberts, D-Camden, led to an eight-day shutdown.

But Weinberg -- who was there for both disputes -- doesn't see a repeat this year.

"I hardly think anything like that will happen," she said.

Republican leaders have praised Sweeney for taking a stand now on taxes.

"I'm deeply concerned the governor doesn't understand how serious the affordability issue is in New Jersey," Assembly Minority Leader Jon Bramnick, R-Union, said Friday. "You're gonna tax more people out of the state."

Bramnick said a millionaires tax is "going nowhere."

"Steve Sweeney is an ironworker," he said of the Senate president, who is also an ironworkers union official. "If he says he's not gonna post a bill, he's not gonna post a bill."

NJ Advance Media staff writer Samantha Marcus contributed to this report.

Matt Arco may be reached at marco@njadvancemedia.com. Follow him on Twitter @MatthewArco or Facebook.

Brent Johnson may be reached at bjohnson@njadvancemedia.com. Follow him on Twitter @johnsb01.