Graham: Stephen Miller makes immigration deal impossible 

GOP Sen. Lindsey GrahamLindsey Olin GrahamSunday shows preview: Trump sells U.N. reorganizing and Kavanaugh allegations dominate Kim, Moon toss ball to Trump in ‘last, best chance’ for Korean peace GOP senator: Kavanaugh accuser 'moving the goalposts' MORE (S.C.) warned on Sunday that the White House staff is undercutting President TrumpDonald John TrumpSunday shows preview: Trump sells U.N. reorganizing and Kavanaugh allegations dominate Ex-Trump staffer out at CNN amid “false and defamatory accusations” Democrats opposed to Pelosi lack challenger to topple her 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 SessionsJefferson (Jeff) Beauregard SessionsDem warns Trump: 'Obstruction of justice' to fire Rosenstein Donald Trump’s Rosenstein dilemma White House proposes executive order to Trump that would examine tech companies’ practices 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.