New Jersey Gov. Chris Christie speaks during the Clinton Global Initiative America's meeting, Friday, June, 14, 2013, in Chicago. (Scott Eisen/AP)

New Jersey Gov. Chris Christie still has a lot to prove to social conservatives if he seeks the Republican presidential nomination in 2016.

A prominent conservative strategist allied with the evangelical movement tells me that both evangelicals and Tea Party activists remain doubtful about Christie. This is partly as a result of his praise for President Barack Obama because of the rapid federal response to Hurricane Sandy last year. Conservatives also raise questions about Christie's commitment to specific conservative principles.

"In the 'tea-vangelical' world, Chris Christie has a lot of work to do," the strategist says.

He adds, however, that Christie actually has a conservative record on issues such as same-sex marriage, abortion, human rights and preserving religious liberty. If he can explain that record effectively to conservatives, he will be a strong contender for the GOP nomination in 2016.

A big problem remains Christie's warm relationship with Obama during the endgame of the 2012 campaign. New Jersey had been hit by the powerful superstorm, decimating many beach communities, and Christie said the federal government was doing good job of providing emergency assistance. But hard-line conservatives were upset that Christie was so positive and they said the governor may have helped Obama, a Democrat, win re-election in the process.

Christie, who is seeking re-election this year, argued that his main priority was helping New Jersey residents, and he was appreciative of the White House's support. He added later that the safety and health of New Jersey residents "are more important than any kind of politics at all."

Last month, Christie turned negative, pointing that he didn't vote for Obama and that the incumbent "can't figure out how to lead" and was more concerned with ideology than "getting things done."

The latest Quinnipiac University poll finds that Christie has a 61 to 29 percent lead over his Democratic challenger, state Sen. Barbara Buono, in his bid for re-election.

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