Senior White House 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 met with moderate Republican senators Wednesday afternoon in an effort to find a resolution to the 19-day partial government shutdown.

Sen. Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.), who hosted the meeting in his Senate Russell Building office for President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE's son-in-law and five other GOP senators, said the Republican lawmakers have agreed on “a process, maybe, that will pay dividends” in finding an end to the standoff between Trump and Democrats over border security.

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Graham said that under a potential deal “the president gets his security funding and can add some things to the mix that would draw some bipartisan support.”

“It’s in its infant stages -- no commitment by anybody -- but I’m somewhat hopeful that maybe there’s a way to get what the president wants in a fashion that would do the least amount of damage to the country,” he said.

Graham summarized the framework as “the wall plus something else” that he hopes would garner some Democratic support.

Sens. Lamar Alexander Andrew (Lamar) Lamar AlexanderTrump health officials grilled over reports of politics in COVID-19 response Now is the time to renew our focus on students and their futures CDC says asymptomatic people don't need testing, draws criticism from experts MORE (R-Tenn.), Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally Gideon leads Collins by 12 points in Maine Senate race: poll Senate leaders quash talk of rank-and-file COVID-19 deal MORE (R-Maine), Lisa Murkowski Lisa Ann MurkowskiGOP ramps up attacks on Democrats over talk of nixing filibuster OVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' House Democrats tee up vote on climate-focused energy bill next week MORE (R-Alaska), Rob Portman Robert (Rob) Jones PortmanRomney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery House passes B bill to boost Postal Service MORE (R-Ohio) and Thom Tillis Thomas (Thom) Roland TillisHillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Republican Senators raise concerns over Oracle-TikTok deal Democratic Senate candidate 'hesitant' to get COVID-19 vaccine if approved this year MORE (R-N.C.) attended the meeting. Collins and Tillis face potentially tough reelection races in 2020.

Murkowski described the meeting as “a group of likeminded senators that are gathering to see if we can’t offer up some helpful suggestions.”

“We’re going to continue the conversations and see where we go,” she said.

Portman said the senators at the meeting were looking for a “reasonable compromise” that would secure the border and let the government fully reopen.

When asked if they had a proposal, Portman said senators are just “talking.”

Kushner declined to comment after leaving Graham’s office.

Democratic senators were not invited.

Jordain Carney contributed.