Sen. Lindsey GrahamLindsey GrahamHigh anxiety for GOP NYC mayor: Trump sounds like ‘a third-world dictator’ Five takeaways from final debate MORE (R-S.C.) said New Jersey Gov. Chris Christie’s “edge” is going to present problems in South Carolina if he decides to run for president in 2016.
"I think he's going to have a hard time in the South, I really do,” Graham told NBC News on Thursday. “The edge is part of it. You know, he's a little too slick by half."
"It seems to me that this whole bridge thing reinforces a narrative that's troublesome about the guy: he's kind of a bully," Graham said.
Graham later told a CNN reporter his criticism on Thursday took place before he saw Christie’s press conference.
“Gov. Christie's response was much different than how the current White House occupant deals with responsibility,” Graham tweeted after seeing the press conference.
Christie fired his deputy chief of staff, Bridget Ann Kelly, on Thursday after emails linked her to the closure of lanes on the state's George Washington Bridge last year. Critics have alleged the closure was political retribution on a Democratic mayor in the area who declined to endorse the governor’s reelection bid.
Christie apologized for the incident during a press conference and said he had no prior knowledge of his staff’s involvement.
The New Jersey governor tried to dismiss the hard-nosed style he has cultivated as governor, at one point saying, “I am not a bully.”
“This is not the tone that I've set over the last four years in this building,” Christie said.
Graham said anyone in his office who did such a thing would have known what was coming.
"I just don't see how people that close to him could have felt comfortable enough to do this if they thought their boss wasn't of this mindset. Isn't that just common sense?" Graham said.
Late last year, The New York Times reported Christie had signaled he would like to help Graham during his reelection bid in 2014. He faces a conservative primary challenger.
Another South Carolina Republican, Gov. Nikki Haley, however, expressed support for Christie after his press conference.
“He did the right thing in taking responsibility in a tough situation,” she said in a Facebook post. “That’s the kind of leadership that earned him the huge level of trust he has in New Jersey.”
— This post was updated at 6:20 p.m.