U.S. Sen. Cory Booker leads his Republican challenger Jeff Bell by 20 points in New Jersey's Senate race according to the latest Monmouth University-Asbury Park Press poll released Wednesday, but a close look at the numbers reveals some red flags for the incumbent Democrat.

U.S. Sen. Cory Booker (Alex Wong, Getty Images)

Among registered voters, 43 percent support Booker while 23 percent back Bell. Democrats say they will vote for Booker at a 73 percent clip, while 61 percent of Republicans said they'll cast their ballots for Bell. Despite Booker's lead, there is reason for some concern in the Booker camp because registered voters aren't as sold on him as they were four months ago.

"On one hand, Cory Booker looks like he's in good position for re-election," said Patrick Murray, director of the Monmouth University Polling Institute. "On the other hand, there's a lot of unsettled voters out there. We also have another 15 percent who say they would vote for another candidate right now, and 17 percent who are undecided."

According to the survey, 1 in 7 voters said they're thinking about voting for a third-party candidate.

Survey respondents were also asked if Booker deserves another term, or if they thought it's time to give someone else a shot.

"Just a few months ago, a solid majority of 55 percent said Booker should be re-elected," Murray said. "It's down to 44 percent right now."

Despite the slip, Booker is getting positive favorability and job performance ratings. By contrast, Bell has a lot of work to do if he wants voters to know him. His name recognition is weak despite the fact that he ran for U.S. Senate in New Jersey in 1978. Right now 12 percent of voters have a favorable view and 6 percent have an unfavorable view of Bell, while 82 percent do not know enough about him to offer an opinion.

The poll also shows New Jerseyans are split when it comes to their opinion of President Barack Obama's job performance. Just 30 percent approve of how Obama is handling the situation in Iraq while 46 percent disapprove. When it comes to the Affordable Care Act, 42 percent have a favorable view while 52 percent have an unfavorable opinion.