The Democratic-controlled state is also poised to play a significant role in the growing resistance to Mr. Trump. The Democratic Party has targeted New Jersey as a state where it hopes to achieve gains in the 2018 midterms. Mr. Murphy’s victory, helped along by strong turnout in the northern part of the state, elevates the chances that incumbent Republican congressmen, like Representatives Leonard Lance and Rodney Frelinghuysen, can be defeated.

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The prospect of a competitive 2018 election loomed larger with the announcement on Tuesday that Representative Frank LoBiondo, a Republican, was retiring at the end of his term, providing Democrats another competitive battleground.

Earlier in the day, Mr. Christie voted in his hometown, Mendham, and, perhaps not surprisingly, gave a local resident a taste of the brash politics that helped make him a national figure.

Victoria Giambra asked Mr. Christie why he hadn’t merged their municipality with the adjoining one — mergers are seen as a way to save money.

“I can’t,” he replied.

But Ms. Giambra pressed him. Mr. Christie grew testy.

“Easier to sit here and complain, but you know what?” Mr. Christie said. “That’s the joy of public service. It’s serving folks like you that is really such a unique joy. You’re fabulous.”

Mr. Christie also stressed that the election was not about him, his policies or his politics.

“My referendum was four years ago,” he said, noting that he won 61 percent of the vote in his re-election. “We’ll see if anybody beats that record any time soon.”

In his speech on Tuesday night, Mr. Murphy never mentioned Mr. Christie. But in an allusion to Mr. Christie’s pugnacious style and the rancor of the Trump era, the new governor vowed to chart a different course.

“Tonight,’’ he said, “we declare the days of division over.”

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