In a brief interview, Mr. Booker said he understood the desire among some Democrats for a more confrontational and combative tone in the Trump era. “I know there’s a lot of folks who may have an appetite for that,” he said. “It’s just not who I am, and I will continue to try to be as fearlessly authentic as I can.”

Will Mr. Booker’s approach work? “If it doesn’t, it doesn’t,” he said.

Mr. Booker has already carried his message to 24 states during the 2018 midterms, including the four that kick off the presidential nominating contest, campaigning for more than 40 candidates and raising more than $7 million for Democratic causes and campaigns, according to his aides. His New Hampshire swing is the last one on the calendar before his self-imposed timeline to make a final decision about running for president.

Back home, state lawmakers have cleared the path for Mr. Booker’s run. In November, the New Jersey governor signed a law that allows Mr. Booker to seek both the presidency and re-election to the Senate in 2020.

There is certainly interest in Mr. Booker: The fire marshal cut off access to Mr. Booker’s speech at the state party’s celebration on Saturday (though the room did not seem particularly full), sending extra people to a nearby overflow room.

Accompanied on Saturday by three aides, Mr. Booker is further along in his New Hampshire outreach than some other would-be candidates. He and his team are reaching out to potential staff, and Mr. Booker has made calls to winners in the midterm elections, which saw Democrats take over both chambers of the State Legislature. Both new legislative leaders got personal calls from Mr. Booker.

Still, few are making any commitments in what is expected to be a crowded field of more than a dozen candidates that could include liberal senators from two neighboring states: Senator Elizabeth Warren of Massachusetts and Senator Bernie Sanders of Vermont, who won the New Hampshire primary in 2016.