"For Newt Gingrich, in an effort of self-aggrandizement, to come out and throw a clever phrase that has no other purpose than to make him sound a little smarter than the conservative Republican leadership, to undercut Paul RyanPaul Davis RyanHouse Dem moves to force vote on bill protecting Mueller Collins: 'Extremely disappointing' ObamaCare fix left out of spending deal House poised to vote on .3T spending bill MORE, is the most self-serving, anti-conservative thing one can imagine happening," Sununu said during the call.

Earlier this year, Gingrich called Ryan's plan "right-wing social engineering." But Gingrich has since apologized for having criticized the plan, and Ryan said Wednesday that he would make a suitable partner in cutting the deficit.

"He misspoke, he acknowledges as much, and let’s leave it at that," Ryan told The Hill.

Romney also launched a television ad Wednesday that plays heavily on his family life — a clear dig at Gingrich, who is twice divorced and has admitted to extramarital affairs.

But Gingrich dismissed questions of whether the attacks had become too personal while campaigning Thursday, saying that Romney was "fine."

Gingrich's thick skin is likely borne out of the robust lead he has built in the polls. A set of CNN polls released Wednesday found the candidate leading by double digits in Iowa, South Carolina, and Florida, while trailing Romney by just 9 points in New Hampshire, long considered a stronghold for the former Massachusetts governor.

-— Erik Wasson contributed to this report.