“Here’s the deal, that mandate is going to fall on the governors,” Mr. Biden told voters. “You saw when he walked out of the Paris accord. It was the governors led by Jerry Brown and others — it was the mayors who said we are not going to go back.”
Former Vice President Al Gore echoed that sentiment when he showed up in New Jersey last weekend to support Mr. Murphy.
“If you want to create the jobs of the future, if you want a governor and a first lady who really get it and who care about clean water and clean air, and cleaning up the climate and provide the jobs in the process, this is a very, very clear choice,” Mr. Gore said at the event in Ocean Township.
Mr. Murphy, a former Goldman Sachs executive and ambassador to Germany, has embraced the party’s emphasis on focusing resistance to Mr. Trump in more liberal states. With Democratic power in the states at a low ebb — there are 15 Democratic governors in the country — Mr. Murphy has promoted a vision of New Jersey as a progressive bulwark, much like other heavily Democratic states, like California and Hawaii.
The only thing standing in the way, Democrats say, has been Mr. Christie, the state’s embattled governor, whom Mr. Murphy’s campaign has targeted as frequently as Mr. Trump.
Mr. Murphy has made trying to preserve Mr. Obama’s accomplishments a centerpiece of his campaign. New Jersey, he said, would join other states in committing to the goals outlined in the Paris climate agreement and to other environmental regulations rescinded by the Trump administration, including rules on clean water.
Mr. Murphy also promised to promote enrollment in the Affordable Care Act after the Trump administration’s move to slash the program’s advertising budget, and he has pledged to defend young undocumented immigrants who might be imperiled by the president’s decision to end the Deferred Action for Childhood Arrivals program, which protected young adults who were brought to the United States illegally as children from being deported.
Mr. Murphy’s Republican opponent, Lt. Gov. Kim Guadagno, by contrast, has received virtually no help from national Republicans, and Mr. Trump and Mr. Christie are so unpopular in the state that their involvement in the race would more likely hurt than help. The disparity in political firepower has appeared to frustrate Ms. Guadagno, who accused Mr. Murphy on Sunday of treating the governor’s race like a campaign for president.
“He’s trying to become the leader of the Democratic Party nationwide,” Ms. Guadagno said in a speech. “He’s even further to the left than any Democrat in New Jersey.”
With his return to retail campaigning, Mr. Obama follows the path of other former presidents, who have ventured out to varying degrees on behalf of candidates after leaving office. George W. Bush, who remained a polarizing figure after he left office, pursued a low-profile role in Republican politics. But Bill Clinton was less restrained, campaigning for Mark Green in New York’s mayoral election in 2001, and going on the road for Democrats in the 2002 midterm elections.
Mr. Obama is unlikely to attack Ms. Guadagno, or to break from his practice of not feuding publicly with Mr. Trump, according to several Obama advisers.
But Mr. Obama will probably stress a list of policy priorities — all stalled or reversed in Washington — that Mr. Murphy might pursue as governor, including stricter gun control laws, more generous health care benefits and additional protections for undocumented immigrants.
In interviews this year, Mr. Obama said he was determined to help rebuild the Democratic Party outside Washington. He appeared at a fund-raiser for the National Democratic Redistricting Committee, a group led by Eric H. Holder Jr., Mr. Obama’s attorney general, that is focused on state legislative elections.
Michael Kempner, a New Jersey public relations executive and Democratic fund-raiser, said the New Jersey elections represented an opportunity for Democrats to play catch-up in the states. The party, he said, had plainly paid too little attention to state politics when Mr. Obama was in office.
“Democrats clearly had their eye off the prize,” Mr. Kempner said. “The states are where things happen, and more and more people understand that.”
Mr. Murphy’s election could make the state a model of “dark blue” policymaking, Mr. Kempner said, noting that the candidate has consistently expressed interest in “how New Jersey and the policies of the state can impact the national agenda.”
Mr. Obama will also campaign in Virginia on Thursday with Lt. Gov. Ralph S. Northam, the Democratic nominee for governor there. But New Jersey represents a distinct opportunity to press a liberal agenda. A victory for Mr. Northam would help Democrats retain a powerful governorship in a key swing state, but Republicans are likely to keep control of the Virginia Legislature, limiting the possibility of enacting an ambitious Democratic agenda.
Mr. Murphy’s potential election, however, would give Democrats full control of New Jersey, making it the seventh state where Democrats hold the governor’s office and both chambers of the legislature and can make policy without Republican input. There are 26 states where Republicans have control of the executive and legislative branches, which has allowed the party to push a sweeping agenda on the state level that has included tax cuts, restrictions on labor unions and new limits on abortion rights.
David Axelrod, Mr. Obama’s senior adviser in the White House, said he expected the former president to stress the stakes of the election to core Democratic voters and “remind them about the hazards of taking elections for granted.”
“Given his role, I would expect him to deliver positive messages about the candidates for whom he’s campaigning rather than negative ones about the opponents,” Mr. Axelrod said.
If Mr. Obama is not expected to take on his successor directly, other visitors to New Jersey have shown no such restraint.
Mr. Biden, in his campaign stop, offered red-meat lines that also were a reality check for liberals seeking to recreate an Obama-era America in blue-state havens.
“Here’s the problem,” Mr. Biden said, “almost no matter what happens, for the next two and half years were going to have a man as president who doesn’t understand America.”
An earlier version of this article misidentified two towns that Joe Biden and Al Gore visited. Mr. Biden was in Edison, not Newark. Mr. Gore was in Ocean Township, not New Brunswick.