Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas) said on Tuesday that a group of Republican senators is drafting legislation that would prevent the separation of immigrant families at the U.S. border with Mexico.

Cornyn, the No. 2 Senate Republican, said the legislation is currently being crafted by a working group of GOP senators, but they are hoping to pitch the Senate Republican Conference on the bill as early as the Tuesday policy lunch.

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"The bottom line is that it would make sure families stay together through the entirety of the legal proceedings and make sure they get an expedited hearing in front of an immigration judge," Cornyn said.

Cornyn's comments come as President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's "zero tolerance" immigration policy along the southern border, which is forcing the separation of migrant families, has sparked high-profile backlash among Republicans. GOP lawmakers are weighing what, if any, action they should take to push back on Trump.

Senate Democrats have united behind a bill from Sen. Dianne Feinstein Dianne Emiel FeinsteinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Democrats shoot down talk of expanding Supreme Court Biden leads Trump by 12 points among Catholic voters: poll MORE (D-Calif.), but Republicans argue that bill is too broad and would result in the release of immigrants trying to enter the United States illegally.

Sen. Ted Cruz Rafael (Ted) Edward CruzCruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP MORE (R-Texas) is expected to introduce his own bill, while Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) said 40 senators approached him to discuss legislation during a Monday night vote series.

Cornyn added that the working group is trying to come up with one bill that could merge the various ideas being bandied about the Republican conference.

"My understanding of what the staff has done is come up with a consensus of all these bills ... that could garner the broader support in our conference," he said. "Ideally, what we'd do is be able to get this hotlined and get it to the president's desk in short order."

He said separately that if they could get enough support for their legislation it could be moved through the Senate "in a matter of days."

But any legislation faces an uphill battle in the Senate. Getting a bill "hotlined" would require the consent of every senator, which could be a political impossibility on an issue as divisive as immigration.

Sen. Tom Cotton Tom Bryant CottonGOP brushes back charges of hypocrisy in Supreme Court fight Trump uses bin Laden raid to attack Biden Battle lines drawn on precedent in Supreme Court fight MORE (R-Ark.), who is a part of Cornyn's working group, separately told radio host Hugh Hewitt that he would try to attach an immigration proposal to a larger appropriations bill being debated by the Senate this week.

"All we need to do ... is overturn the so-called Flores Settlement, allow families to be held at the border, provide a little bit of extra money to the military and [Department of Homeland Security] for family housing units while those claims are adjudicated," he said.

Cotton added that "we’re going to offer an amendment this week on the spending bill. It can be done promptly."