So Democrats are in charge of everything in New Jersey government for the first time this decade, and progressives who chafed under two terms of Chris Christie couldn't be happier.

For eight years, they took aim at the Republican governor for paltry investments in everything from schools and safety net social programs to public transit and government worker pensions. They charged that New Jersey was failing its neediest while heaping subsidies on wealthy corporations and waited for the day they could check off some boxes on their liberal wish lists.

And now with Democratic Gov. Phil Murphy ready to deliver his first state budget address to a state Legislature run by his party, there will be peace and tranquility in Trenton. Right?

Don't bet on it.

Tuesday's budget address, a blueprint for how the new governor plans to spend taxpayer money to mold New Jersey in his progressive image, could set in motion a brewing all-Democratic Party fight over just who should pay the bills: corporations or millionaires.

Murphy is expected to call for a heightened tax on millionaires, but he's in for a tough time winning over state Senate President Stephen Sweeney, D-Gloucester, and state Assembly Speaker Craig Coughlin, D-Middlesex.

The millionaires tax is essential to Murphy's game plan for increasing funding to the school funding formula, which is underfunded by about $1 billion a year.

New Jerseyans with income over $1 million would find themselves in a new 10.75 percent marginal tax bracket, estimated to kick up more than $600 million in tax revenue for cash-starved state coffers.

The state's personal income tax rate currently tops out at 8.97 percent on income over $500,000.

"It comes down to asking, do we continue to hollow out the very core of our state, of our society, or do we ask the wealthiest and biggest corporations to pay their fair share and then invest those proceeds in things that we know grow an economy: education, infrastructure and tax relief for our middle-class, working families and seniors," Murphy said in a speech at a New Jersey Chamber of Commerce dinner earlier this month in Washington.

"We tried the first option for eight years," he continued. "It left us with a lagging economy, crumbling infrastructure, underfunded schools and rising property taxes for middle-class families."

Gordon MacInnes, president of a left-leaning Trenton think tank and a former state legislator, is one of those progressives who say the Garden State's assets have been neglected.

"Governor Murphy may have the will and courage to say it's time to turn the state around," MacInnes said Friday.

More than will and courage, Murphy needs money. And Sweeney, the most powerful man in the Legislature, says it shouldn't come from millionaires' pockets.

Flashback to November, a millionaire's tax was pretty much inevitable. Sweeney had put the tax hike on Christie's desk five times, forcing his veto over and over.

The morning after Murphy's win, Sweeney tweeted that the "long-overdue millionaires tax" would be "the first bill we pass in January."

But when Congressional Republicans started eyeing elimination of the state and local tax deduction to pay for corporate tax cuts, the south Jersey Democrat took his foot off the gas.

In December, President Donald Trump, a Republican, signed a tax law putting a $10,000 cap on the tax deduction, and Sweeney said New Jersey couldn't risk doing tax-fatigued millionaires more harm.

"It's the absolute last thing that I'm willing to look at," Sweeney said last month. "It's too much right now. Absolutely last resort."

Then last week Sweeney introduced his own attention-grabbing plan to impose a 3 percent surcharge on New Jersey's businesses with net income over $1 million.

New Jersey businesses will save $2.9 billion annually as a result of Trump's corporate tax cut, and the state can grab more than $600 million of that to fund special education, expand pre-K and help underfunded school districts, Sweeney said.

Unmoved, Murphy said he didn't consider the corporate tax hike an alternative to a millionaire's tax. If anything, the governor added, it's another potential pot of money.

Assembly Minority Leader Jon Bramnick, R-Union, painted the conflict as a battle between a veteran legislator and a new governor who had never held elected office.

"I think Steve Sweeney has a lot of experience," Bramnick said Friday. "Unfortunately, Governor Murphy doesn't have a lot of experience. I think when inexperience clashes with experience, it's not always pretty."

Ultimately the lawmakers will have to cut a deal or risk another one of those state government shutdowns. Sweeney and Coughlin control the Legislature, but Murphy possesses a powerful line-item veto.

MacInnes said he's actually encouraged by Sweeney's competing proposal, saying it alleviated some fears he was going shun new taxes altogether in the wake of federal tax reform.

"I think they're thinking along parallel ways," he said. "Maybe that's opening the door for negotiation and closer agreement. I see it as a promising opportunity."

MacInnes said Murphy should "probably include both proposals as a starting point, and maybe more than that."

For his part, Coughlin, the new and untested Assembly speaker, says lawmakers' priority should be reducing spending and better managing existing revenue "before we raise taxes on anyone."

Bramnick said he's not surprised to see this fight brewing.

"I would expect Democrats to fight over which taxes to raise," he said. "Maybe all of a sudden, we're starting to miss Chris Christie a bit. It's who's gonna pay more: the job creators or the individuals?"

Samantha Marcus may be reached at smarcus@njadvancemedia.com . Follow her on Twitter @samanthamarcus. Find NJ.com Politics on Facebook.

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