“The problem is in New Jersey or at any state level, maybe you’ve seen different math than I have, but it’s jaw-droppingly expensive,” he said referring to health care. “Are we open to it at the state level? Absolutely. But it’s billions of dollars a year.”

The same goes for education. He embraces fundamental progressive ideas, like universal preschool and tuition-free community college.

But only once the economy improves.

“If we are able to grow at this rate, and find these sources, we’re left with surpluses,” he said, explaining the economic expansion he believes will take place under his policies. “So we want to also take that and the first steps toward phasing in universal pre-K and free community college.”

Mr. Murphy’s campaign is filled with big promises and occasional murky financing to back it up. He wants to fully fund the state’s pension liability, provide public schools all the state aid they are due and pay down health care liabilities for state workers, all of which are a large part of the state’s $35 billion debt.

He says that he can pay for this in part by raising taxes on the wealthy, closing corporate loopholes, and legalizing and taxing marijuana. That combination would yield just over $1 billion, according to reports, while the balance would come from the rosy economic outlook Mr. Murphy says his policies will generate.

Running alongside his progressive streak is a degree of pragmatism. He counts Lyndon B. Johnson as a political role model, along with Robert F. Kennedy. He admires Mr. Kennedy for his “calls to service,” and Mr. Johnson for his accomplishments.

“All that ideology is well and good, but Lyndon Johnson got stuff done,” he said. “This state needs a leader who not only stands for the right things but gets stuff done.”