Former Florida Gov. Jeb Bush's exploration of a possible a run for the White House in 2016 makes a Chris Christie presidential bid "a difficult shot," one New Jersey political analyst says.

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"He (Christie) actually has a shot at winning it," said Patrick Murray, director of the Monmouth University Polling Institute. "The shot is very difficult and it involves threading the needle in a way that he was going to have to do before, but even more so now because both Jeb Bush and Chris Christie are going to try and get through the same needle eye."

Christie is still one of the best-known and top Republican contenders in the country, but he will have to overcome his high unfavorable ratings among GOP voters nationwide Murray noted.

And courting the party's conservatives might not work for Christie.

"The problem with Gov. Christie veering right is that the right has already decided that they don't trust him so going there would actually increase their distrust," Murray said.

The governor also has a brand to protect, according to Murray, and veering to the political right would likely hurt that brand which has been extremely strong.

"Christie has this brand as the problem solver, the fixer, the person who can reach across the aisle either with his hand or with a hammer, whichever it takes to get something done and veering to the right is just going to totally undermine that," Murray said.