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 (R-S.C.) said Friday that Sen. Tom Cotton Tom Bryant CottonRenewed focus on Trump's Supreme Court list after Ginsburg's death Republicans call for DOJ to prosecute Netflix executives for releasing 'Cuties' Loeffler calls for hearing in wake of Netflix's 'Cuties' MORE (R-Ark.) has become "sort of the Steve King Steven (Steve) Arnold KingGOP leader: 'There is no place for QAnon in the Republican Party' Loomer win creates bigger problem for House GOP Win by QAnon believer creates new headaches for House GOP MORE of the Senate," a reference to one of the House's most ardent immigration hard-liners.

In an interview with MSNBC, Graham, who has advocated for legislative protections for young immigrants, rejected the notion of ending family-based immigration in exchange for enshrining the protections of the Deferred Action for Childhood Arrivals (DACA) program into law.

A proposal by Cotton and Sen. David Perdue (R-Ga.) seeks to end so-called chain migration, which allows U.S. citizens and permanent residents to sponsor family members abroad to come to the U.S.

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"All I can say is we're not going to end family immigration for DACA," Graham said. "The Tom Cotton approach has no viability here. You know, he's become sort of the Steve King of the Senate."

"I like Tom, but on immigration, he's putting something on the table that there's just no market for in Phase 1," he added.

King, an Iowa Republican, has been a vocal advocate for curbing immigration and ending DACA, an Obama-era program rescinded by Trump last fall.

Graham's comments came as lawmakers barrel toward a government shutdown amid a struggle to reach an agreement on a spending measure to keep the government running past Friday.

Democrats have insisted that any spending measure must include protections for DACA recipients, while some Republicans have called to address legal protections for the young immigrants, known as Dreamers, at a later date.