GOP Sen. Lindsey Graham Lindsey Olin GrahamMomentum growing among Republicans for Supreme Court vote before Election Day Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Warning signs flash for Lindsey Graham in South Carolina MORE (S.C.) warned on Sunday that the White House staff is undercutting President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE and Congress's ability to get a deal on immigration.

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"Every time we have a proposal it is only yanked back by staff members. As long as Stephen Miller is in charge of negotiating immigration, we're going nowhere," Graham told reporters as he headed into a closed-door negotiation with a bipartisan group of senators.

He added that "the White House staff, I think, is making it very difficult."

Miller, a White House aide, is well known for his conservative views on immigration. He was formerly a staffer for then-Sen. Jeff Sessions Jefferson (Jeff) Beauregard SessionsTrump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status White House officials voted by show of hands on 2018 family separations: report MORE (R-Ala.), who frequently opposed bipartisan immigration deals.

Miller authored the White House's wide-ranging immigration plan, which includes wall funding and cracking down on cities that don't comply with federal immigration law.

Graham said on Sunday that Miller has "been an outlier for years" on the issue of immigration.

The White House fired back at Graham.

"As long as Senator Graham chooses to support legislation that sides with people in this country illegally and unlawfully instead of our own American citizens, we are going nowhere. He’s been an outlier for years," said White House spokesman Hogan Gidley.

Democrats have repeatedly bristled at Miller's involvement in the immigration talks, arguing he isn't a constructive force in the immigration talks.