Story highlights Conway says Trump supporters feel "betrayed"

Mitt Romney is being considered for Secretary of State

(CNN) President-elect Donald Trump is "irritated" with top aide Kellyanne Conway's public campaign against Mitt Romney's potential nomination as Secretary of State, according to a source.

The Trump source, who is familiar with the President-elect's thinking, acknowledged the existence of an internal feud between Conway and chief of staff Reince Priebus, specifically about the choice between Romney and former New York City mayor Rudy Giuliani for the nation's top diplomatic position.

JUST WATCHED Conway questions Romney's loyalty to Trump Replay More Videos ... MUST WATCH Conway questions Romney's loyalty to Trump 03:23

The strange feud playing out in public between Romney and Giuliani has captured the attention of the nation in a way rarely seen after the election ends and the transition to the White House begins.

Conway told CNN that she has spoken to Trump several times, both yesterday and today, and that he was not angry or irritated.

Conway, who is in Trump Tower today, said Trump understands that her comments about Romney come from a place of loyalty to the President-elect.