Forty-six percent of the respondents support Kerry, 43 percent back Bush, and 5 percent would vote for independent candidate Ralph Nader (search). The poll, released Thursday, has a sampling error margin of plus or minus 3 percentage points.
Among independent voters polled, the major party candidates are statistically tied in the race for New Jersey's 15 electoral votes.
Kerry's favorability is poor in New Jersey, which Al Gore won by 16 percentage points in 2000. Twenty-seven percent approve of the Democrat, 28 percent don't and 33 percent are mixed, according to the poll.
"Despite all the bad news out of Iraq, President Bush is threatening to make a horse race out of New Jersey, a state everyone had put in the 'safe' column for John Kerry," said Clay F. Richards, assistant director of the Quinnipiac University Polling Institute (search).
Bush's approval rating remains unchanged from the previous Quinnipiac poll in March, with 52 percent disapproving and 44 percent approving.
Respondents believe Bush would do a better job of handling the war while Kerry's strength is the economy.
The telephone survey of more than 1,100 registered voters was conducted May 10-16.