Of those three states, Mr. Christie, who has yet to formally enter the race, drew double-digit support only in New Hampshire in NBC News/Marist polls released Sunday. By contrast, former Florida Gov. Jeb Bush and Wisconsin Gov. Scott Walker had support above 10% in all three states.

An early test of Mr. Christie’s appeal came on Monday, when he spoke at a Republican dinner in Concord, his first appearance in New Hampshire this year.

“He should spend a lot of time in New Hampshire,” said Matt Mackowiak, a Republican strategist based in Texas, who believes Mr. Christie will be seen as too centrist in Iowa and South Carolina. “You have to start winning primaries at some point and accumulating delegates. Your own supporters will start to move somewhere else otherwise.”