Story highlights "There are people in the White House who are outliers," Graham said

Last week, Graham presented a bipartisan immigration deal to the White House

Washington (CNN) Sen. Lindsey Graham said Thursday that some of President Donald Trump's White House staff have "irrational" views on immigration, continuing his criticism of how the White House has handled delicate negotiations on the matter.

In making the case to CNN's Dana Bash that Trump isn't well served by his own administration, Graham is apparently trying to circumvent the White House to appeal to the President himself as Congress nears a shutdown due, in part, to disagreements about immigration.

"There are people in the White House who are outliers," the South Carolina Republican said in an exclusive interview. "There are people around the President who have an irrational view of immigration. They always have, and if you follow that lead we'll never get anywhere."

Last week, Graham presented a bipartisan immigration deal to the White House alongside Sen. Dick Durbin, D-Illinois. Trump rejected the deal. Durbin this week said "any attempt to kill immigration reform probably has (White House senior adviser Stephen) Miller's fingerprints on it." Miller, who was at the deal's presentation at the White House, and is one of the administration's most conservative members on immigration.

Earlier this week, Graham told reporters that Trump was "not well served by his staff" on the immigration debate. Asked about chief of staff John Kelly specifically, Graham called him a good man but noted that he is a member of the staff, and added that some at the White House have "an irrational view."

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