Christie challenge: Unite tea party and big money

Christie's run to the White House

If newly re-elected New Jersey Gov. Chris Christie runs for president in 2016, his ability to deal with the national scrutiny of his background and the deeply divided Republican Party will be key factors to the success of his possible candidacy, the authors of the new book "Double Down" told CNBC.

"Navigating the Republican Party, that's the biggest challenge not just for Chris Christie but for anybody," Mark Halperin said in a "Squawk Box" interview, promoting the book with co-author John Heilemann. "Christie needs to navigate the tea party and the big money people and bring them together."

In Tuesday's election, Christie easily won a second term by defeating Democratic challenger and state senator Barbara Buono.

(Read more: Christie wins big, tea party loses in Va. race)

"People think they know a lot about Chris Christie because he's gotten a lot of attention for a governor. The truth is there's been very little national scrutiny to the totality of his background," said Heilemann.

"He's going to get a lot more attention than he's ever gotten before, and we'll see how he stands up to that."

(Read more: Chris Christie could save the GOP)

Gov. Chris Christie arrives to speak at his Election Day victory party Tuesday night.
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Christie, a former prosecutor, is known for his for his blunt manner and speaking his mind—sometimes with seemingly little regard for the political consequences.

The New Jersey governor's embrace of Barack Obama last year, during the president's tour of the damage in the Garden State from Superstorm Sandy infuriated many national Republicans. They thought it hurt Mitt Romney days later at the ballot box.

(Read more: Op-ed: What the GOP needs to do to win elections)

"I hear all the time from Republicans, both the billionaire donors in some categories and also the grassroots," Halperin said. "That's going to be a high hurdle for him to get over."

On NBC's "Meet the Press" last Sunday, Romney said Christie has a great track record with a "demonstrated ability to work across the aisle."

The interview followed an excerpt from "Double Down" released by TIME on Saturday, which detailed health concerns, punctuality problems, and other issues that were factors in Romney's decision not to pick Christie as his vice presidential running mate in the 2012 election.

Romney said on NBC that his researchers didn't uncover anything that "wasn't already part of the public record and that hadn't already been dealt with effectively" by the Christie camp.

Heilemann told CNBC: "It was the sum and substance of the whole thing that made Romney pull the plug on Christie."

On CNN Tuesday, Christie said Romney called right away about the leaks and was "really embarrassed and outraged. Christie also said he was "very disappointed" by the revelations in the book, and felt they were a "complete violation."

—By CNBC's Matthew J. Belvedere. Follow him on Twitter @Matt_SquawkCNBC. Wire services contributed to this article.