The White House has said it is willing to extend the partial government shutdown, now in its third week, for months and even years in order to secure funding for a southern border wall.

And one of President Donald Trump's most ardent advocates in the Senate amid his battle with congressional Democrats also appeared ready to accept a long-term shutdown to achieve the president's goal.

"I do want to open up the government, but the goal is not to open up the government," Sen. Lindsey Graham said Sunday on CBS' "Face the Nation" when asked if he would support opening up the government before continuing negotiations.

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"The goal is to fix a broken immigration system to bring reality to this table," the South Carolina Republican said. And after speaking to Trump, Graham said, "it was pretty clear to me that we're never going to have a deal unless we get a wall as part of it."

House Democrats led by Speaker Nancy Pelosi, D-Calif., have said they will not negotiate on border security funding until the government is reopened.

Immediately before Graham's appearance, Sen. Dick Durbin, D-Ill., told "Face the Nation" host Margaret Brennan that "there is no requirement that this government be shut down while we deliberate the future of any barrier, whether it's a fence or a wall."

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"Dick Durbin is a reasonable guy, but he's not leading this parade," said Graham, who joined Durbin last year in proposing an immigration deal that included $25 billion in border security, but was rejected by the president.

Graham said the left-wing of the Democratic party is leading the fight against Trump's request for $5.6 billion in border security – primarily, to build a wall – and they are not acting as reasonable partners in negotiations.

"As long as the radical left is in charge we're never going to get anywhere. The president will compromise, but he will not capitulate," Graham added.

He repeated his belief that the "president is right to dig in to get money for a wall as part of border security." Last week, Graham said that caving in on this fight could spell the end of the presidency for Trump, who made the wall a central campaign promise.

Graham said that the president might consider a deal granting citizenship to some immigrants, such as the undocumented DREAMers who came to the U.S. as children, in exchange for border security funds. But Graham said those negotiations can't take place until Democrats like Durbin, rather than Pelosi, lead the negotiations.

"We're not going to put any offers on the table as long as people in charge of these negotiations accuse all of us who want a wall of being a racist and see our Border Patrol agents as gassing children," Graham said. "Until you get that crowd put to the sidelines, I don't see anything happening."

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