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."