The president also enjoys a strong favorability rating of 58 percent in the state.
He has slightly more support in the more Democratic-leaning seven counties that comprise South Jersey, with 53 percent planning to vote for Obama and 38 percent for Romney. The president's 15-point lead there was down from 22 in the previous month's survey.
The poll results are the latest sign that New Jerseyans won't be besieged by the campaign ads that are now blanketing states like Ohio and Florida. The state is firmly in the Obama column, and both campaigns seem to have tacitly acknowledged that.
The Democratic pollster on the Inquirer poll, Jeffrey Plaut of Global Strategy Group, said that while Romney won the Oct. 3 debate, Obama had built a solid lead after the previous major campaign event: the conventions.
Now, Plaut said, polls are returning to closer margins seen earlier in the summer.
"The debate is not the only piece of data voters used to make up their minds," Plaut said. "It's an important one, but Obama voters can say: 'Romney won the debate, but I'm still with Obama.' "
The Republican pollster on the survey, Adam Geller of National Research, said Obama could slip even further in the coming weeks, and the debate performance could hurt Democratic turnout Nov. 6.
"Does it mean that the bleeding is done?" Geller asked. "Not necessarily." He said Obama could win the state by just four or five points.
For its part, the Obama campaign said it would not take New Jersey for granted. "Our campaign will continue to focus on expanding our volunteer base and reaching out to voters across the state to make clear the contrast that exists for New Jersey voters," said Geoffrey D. Borshof, the campaign's state director.
Last week's debate had strong viewership in New Jersey. Eighty-two percent of poll respondents said they watched at least part of it; 24 percent said they read or posted social-media comments about it.
And it may have influenced some decisions: 35 percent said that the debate left them more likely to vote for Romney - while 62 percent said it either left them less likely to vote for him or did not change their minds. Likewise, 33 percent said they were less likely to support Obama afterwards; 64 percent said it made them more likely to vote for him or made no difference.
This reflected a post-debate trend throughout the country in which Romney gained ground and now has a narrow lead in several national polls. The Inquirer's post-debate poll in Pennsylvania had Obama leading there by 8 points, compared with 11 last month.
Romney is now honing in on several swing states to take advantage of his performance. This week, he brought in Gov. Christie - considered one of the candidate's best surrogates - for two days' campaigning in Ohio. It was Christie's first appearance with Romney on the trail since the August convention.
Christie scored well in the New Jersey poll, with 59 percent favorability among men and women alike. That was an improvement for him with his female constituents.
In Ohio, he and Romney hosted a town-hall-style meeting in which Romney fielded questions and Christie sat on a stool and occasionally amplified points.
In his appearances Christie focused on a statement made in a video that aired at the Democratic convention: "Government is the only thing we all belong to."
"We don't belong to the government," Christie said. "The government belongs to us."
On a conservative radio show Wednesday, he also defended Romney from criticism on the right that he is not sufficiently pro-life. And at a rally, he predicted that Obama would get "pretty mean" and "pretty angry" in the remaining weeks of the campaign.
Christie is scheduled to be back in New Jersey on Thursday for a 3 p.m. town-hall meeting at the Mount Laurel YMCA. He generally talks about local issues at these events, however. And he has acknowledged that Romney can't win his state.
Obama bests Romney in virtually every category of New Jersey voters, including women, those without a college degree and younger voters, according to The Inquirer's poll.
On the issues, voters said they trusted Obama more on education, Medicare and taxes. They were divided about who can do better on jobs and the economy, while Romney is viewed as better able to handle the federal deficit.
"I think Romney has a golden tongue when it comes to talking about taxes and the economy," said Ronnie Brunker, 75, of Haddonfield, one of those surveyed.
An Obama supporter who thought the president was "abysmal" in the debate, Brunker said Romney was more accustomed to talking economic issues - "it's his forte."
"Sitting there, you hear him throwing all these words around, I would say three-quarters of the people watching it didn't have any idea what he was saying," she said. "But he said it with force, which was what was important, and perceived knowledge."
Romney didn't have to convince Michael Dauber, the deputy mayor of Bordentown and another of those polled.
"He didn't have to sway me because there was no way I was going to vote for Obama anyway," Dauber said.
One of his biggest beefs with Obama is how, in Dauber's view, the president had "apologized" for America after getting into office.
As an officeholder, Dauber said he has found that "in the public sector it just takes too long to do things sometimes." So a business sensibility such as Romney's is needed to straighten things out, he said.
"When you start bringing those principles into government, you can really make it work," Dauber said.
Self-described Obama "diehard" Nicole Moore Samson of Mount Laurel, another poll participant, was also unswayed by the first debate. But "I'm just so angry with him a week later that this huge lead he had, he lost," said the 43-year-old elementary school principal.
She said Obama should have cited Romney's taped remark about not caring about 47 percent of Americans - and should have shown "a little more grit." On that score, at least, she said Obama "could use a little bit" of Christie.
While Samson disagrees with "everything Mr. Christie says and does," she admires that the Republican governor is "not afraid of letting everybody know he's in charge."
Contact Matt Katz at 609-217-8355 or firstname.lastname@example.org, or follow on Twitter @mattkatz00. Read his blog, "Christie Chronicles," at www.philly.com/christiechronicles