An internal dispute among Donald Trump's advisers broke out into the open on Sunday when his campaign manager warned that the president-elect could face an intense backlash from supporters if he chose Mitt Romney to be his secretary of state.

Trump has been weighing whether to pick Romney, the 2012 Republican presidential nominee who spent much of the past year criticizing Trump, or former New York City mayor Rudy Giuliani, who backed the real-estate mogul's insurgent presidential run.

Giuliani would fit with the other loyalists and conservative hardliners that Trump has picked to fill out his administration so far, but he has drawn criticism for working as a consultant to foreign governments.

Trump could help unite his party and win over skeptical establishment Republicans if he chooses Romney for the post.

Though the debate has largely played out behind closed doors, campaign manager Kellyanne Conway warned that Trump could anger his supporters if he picked Romney, who called him a "fraud" and a "phony" in speeches this year.

"They feel betrayed to think that you can get Romney back in there after everything he did - we don't even know if he voted for Donald Trump. He and his consultants were nothing but awful to Donald Trump for a year," she said on NBC's "Meet the Press."

"I am all for party unity but I am not sure that we have to pay for that with the Secretary of State position," Conway said on CNN.

Conway said she would support Trump if he decided to pick Romney for the position, but other Republicans criticized her for making her case on television, rather than talking to Trump directly.

"Astounding to hear K. Conway, who has the ability to tell Trump privately, trash possibility of Romney as Sec of State publicly," Republican strategist Ana Navarro wrote on Twitter.