Acting White House chief of staff Mick Mulvaney Mick MulvaneyMick Mulvaney to start hedge fund Fauci says positive White House task force reports don't always match what he hears on the ground Bottom line MORE in an interview broadcast Sunday downplayed the significance of pressure from President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE's more conservative supporters to follow through on a pledge to build a wall along the U.S.-Mexico border.

"Meet the Press" anchor Chuck Todd questioned Mulvaney over why Trump can't compromise on the wall in the face of criticism over any deal from conservative media personalities like Sean Hannity and Ann Coulter, and Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans signal openness to working with Biden Loeffler calls for hearing in wake of Netflix's 'Cuties' Quinnipiac poll shows Graham, Harrison tied in South Carolina Senate race MORE (R-S.C.).

"I would make the argument that the president has probably more sway over Sean Hannity and Ann Coulter than vice versa," Mulvaney said.

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"And you know that I like Lindsey Graham and he's a good friend of mine," he added. "We're from South Carolina. He’s not as good a politician as Donald Trump or else he'd be president. They both ran and one of them won and one of them lost."

Graham said last week that Trump could not afford to cave on his fight for a border wall, warning that if he gave in, "that's the end of 2019 in terms of him being an effective president."

Mulvaney insisted on Sunday that Trump is "interested in resolving" the partial government shutdown, which has lasted 16 days and counting. The impasse has been spurred by Trump's demand for $5 billion in funding for his proposed border wall, while Democrats have refused to offer any money for the structure.

Mulvaney, Vice President Pence and other White House aides met with congressional leaders' staff on Saturday, and are expected to do so again on Sunday.

Trump has offered shifting messages on the wall as the shutdown drags on, claiming at various times that Congress must fund the wall, that the structure is already largely built and that Mexico will pay for it over time. The wall, however, has not been built and Mexico has said it will not fund the project.