Graham: Stephen Miller makes immigration deal impossible 

GOP Sen. Lindsey GrahamLindsey Olin GrahamOvernight Health Care: Watchdog finds Tom Price improperly used funds on flights | Ex-Novartis CEO sent drug pricing proposal to Cohen | HHS staffers depart after controversial social media posts HHS staffers depart after controversial social media posts: report Senate takes symbolic shot at Trump tariffs MORE (S.C.) warned on Sunday that the White House staff is undercutting President TrumpDonald John TrumpSasse: Trump shouldn't dignify Putin with Helsinki summit Top LGBT group projects message onto Presidential Palace in Helsinki ahead of Trump-Putin summit Hillary Clinton to Trump ahead of Putin summit: 'Do you know which team you play for?' 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 SessionsConservatives moving to impeach Rosenstein soon: report Senators urge DOJ to probe whether Russians posed as Islamic extremist hackers to harass US military families The Hill's Morning Report — Trump readies for Putin summit: 'He’s not my enemy’ 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.