But Mr. Bramnick, who at times has been critical of Mr. Trump, believes that the shift to the left could help increase support for the Republican Party, and he has been trying to appeal to moderate voters and the state’s significant number of independents under the banner of “rallying the reasonable.”

“Is this kind of extreme politics good for Republicans?” he asked. “It is.”

While New Jersey has become increasingly blue over the years, it has tended to be more moderate than other Democratic-leaning states with wide swaths of the state, including counties along the shore, remaining Republican strongholds.

At the same time, it is reliably progressive on social and environmental issues, with residents favoring the legalization of recreational marijuana and embracing climate change as an irrefutable fact at a higher rate than people nationwide, according to a Yale University study.

Still, even as the state veers left, there are some measures that New Jersey residents simply will not stomach, particularly if they are forced to pay even more in taxes. And without new revenue or painful cuts, Mr. Murphy will be hard pressed to realize his far-reaching goals.

“The reason why Phil Murphy can make this a liberal laboratory here in New Jersey right now is because there’s no strong organized opposition to him,” said Patrick Murray, the director of the Monmouth University Polling Institute. “But he could be in for a rude awakening when we get to the issue of core taxes and property taxes.”

Mr. Murphy said he was willing to negotiate any part of his proposed budget, which must be signed by June 30, but he believes government is essential to the lives of his constituents. Having grown up in the 1960s, Mr. Murphy said that the era of his childhood, when “the government put a lot of wind in your sails,” helped cement his view that raising taxes and investing more in government was the best use of people’s money.