Story highlights The poll, released Tuesday, finds Clinton beating Trump 38%-34% if the election were held today

A sizable group (15%) also said it would vote for alternatives

Washington (CNN) Hillary Clinton is edging out Donald Trump in New Jersey, but a sizable group of voters is looking for alternatives to each major party candidate, according to a new poll from Monmouth University.

The poll, released Tuesday, found Clinton beating Trump 38%-34% if the election were held today. A sizable group (15%) also said it would vote for alternatives, including Libertarian nominee Gary Johnson (5%), Green Party candidate Jill Stein (4%) or some other, unnamed alternative (6%).

"Blue Jersey doesn't appear quite so blue at this stage of the campaign, but we should keep in mind that neither major party candidate has fully locked in the support of their partisan bases. When and if that happens, the benefit should accrue more to Clinton than to Trump simply because Democrats outnumber Republicans in the state," Patrick Murray, director of the independent Monmouth University Polling Institute, said in a statement.

The poll appears to lend some credence to the argument made by Johnson -- who won the Libertarian nomination over the weekend -- that the deep unpopularity of both Clinton and Trump makes it a opportune time for a third-party candidate. Johnson mocked Trump on CNN's "New Day" on Tuesday, blowing him a kiss as he knocked the presumptive GOP nominee's statements on immigration.

The poll also contains some bad news for New Jersey Gov. Chris Christie: 42% of voters said if Trump added him to the ticket, they would be less likely to support the pair. (About half of voters -- 48% -- said a Trump-Christie ticket would not impact their decision and 8% said it would make them more likely to vote Republican.)

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