As Gov. Christie courts Republicans across the country -- most recently in Iowa -- a new poll suggests he faces an uphill battle.

More than half -- 57 percent -- of Republican primary voters surveyed in an NBC News/Wall Street Journal poll released Monday could not see themselves supporting Christie for the GOP presidential nomination in 2016, compared to 32 percent who could.

That gap placed Christie behind other well-known prospective Republican candidates in the poll, including former Florida Gov. Jeb Bush. Of Republicans surveyed, 49 percent could see themselves supporting Bush, while 42 percent could not.

Leading the poll were two Republicans with less name recognition: Florida Sen. Marco Rubio, with 56 percent of Republicans saying they could see themselves supporting him and 26 percent saying they could not; and Wisconsin Gov. Scott Walker, with 53 percent supporting and 17 percent not.

Rubio was unknown to 14 percent of Republicans surveyed, and Walker to 27 percent. Christie was known by all but 7 percent of Republicans.

The poll, conducted March 1-5, included 229 Republican primary voters. The margin of error for their responses is 6.48 percent.