White House senior adviser Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE briefed the Senate GOP conference Tuesday on the White House's plan to overhaul legal immigration as part of an effort to build support for the forthcoming proposal.

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"I don't think it's designed to get Democratic support as much as it is to unify the Republican Party around border security," he said.

Graham added that the White House was trying to unify Republicans around a "negotiating position" that would allow the party to say "this is what we want on border security. This is what we want on merit-based immigration and then we'll have to sit down and find common ground on the 11 million."

The meeting with the full Republican conference comes after roughly a dozen GOP senators went to the White House earlier this month to discuss legislation to transition the system for legal immigration to a "merit-based" system.

The White House proposal, which was spearheaded by Kushner, would not cut the total number of legal immigrants, roughly 1.1 million, accepted into the United States every year. Instead, senators say it would try to shift the federal government's preference for who gets green cards to those with specific job skills instead of family-based immigration.

But any immigration proposal faces uphill odds on Capitol Hill, where multiple pieces of legislation have failed in both the House and Senate.

"There was a lot of encouragement in the room today for the work they've done," he said. "A lot of encouragement."