Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) on Monday promised to take up an immigration bill protecting an estimated 800,000 "Dreamers" from deportation and allow an open amendment process if Democrats agree to reopen the government.

The Senate will vote at noon on a three-week funding resolution to end the government shutdown that began at midnight Saturday. The legislation includes an extension of the Children’s Health Insurance Program (CHIP).

ADVERTISEMENT

Democrats have been pressing McConnell for a vote on the Dreamers legislation, and it is unclear whether his latest commitments will be enough to win them over.

With some Republicans expected to vote against the bill, nearly a dozen Democratic votes will likely be needed to clear a 60-vote procedural hurdle.

Senate Democrats and Republicans will try to negotiate an immigration compromise before the pending stopgap measure would expire on Feb. 8, if that stopgap is approved.

If they fail to reach a deal, McConnell promised he will bring an immigration bill to the floor in February.

But McConnell said his promise would only be good if Democrats agree to reopen the government.

“Should these issues not be resolved by the time the funding bill before us expires on Feb. 8, so long as the government remains open, it would be my intention to take up legislation here in the Senate that would address DACA, border security and related issues as well as disaster relief,” McConnell said, referring to the Deferred Action for Childhood Arrivals program started by President Obama that President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE is winding down.

The GOP leader pledged “this immigration debate will have a level playing field at the outset and an amendment process that is fair to all sides,” he said.

Behind the scenes, a group of centrist Democrats and Republicans have been trying to work out a deal on immigration.

Democrats leaving a meeting of moderate senators on Monday morning said they are still discussing how to get a firmer commitment for a vote to protect young immigrants in the country illegally.

"We just need a commitment on that that's firm, that we know we're going to be on it, the question is how firm the commitment [will be]" said Sen Tim Kaine Timothy (Tim) Michael KaineBarrett seen as a front-runner for Trump Supreme Court pick Biden promises Democratic senators help in battleground states Second GOP senator to quarantine after exposure to coronavirus MORE (D-Va.) leaving the meeting in Sen Susan Collins Susan Margaret CollinsJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally Momentum growing among Republicans for Supreme Court vote before Election Day MORE's (R-Maine) office.

Sen Amy Klobuchar Amy KlobucharThe Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill EPA delivers win for ethanol industry angered by waivers to refiners It's time for newspapers to stop endorsing presidential candidates MORE (D-Minn.) said they need a "real commitment" to bring up an immigration bill.

No Democrats said leaving the meeting that they are changing their votes. Though when asked how he would vote at a noon vote on Monday, Sen Bill Nelson Clarence (Bill) William NelsonDemocrats sound alarm on possible election chaos Trump, facing trouble in Florida, goes all in NASA names DC headquarters after agency's first Black female engineer Mary W. Jackson MORE (D-Fla.) said he thought that vote could be postponed if negotiators need more time.

Republicans who attended the meeting said McConnell should have been more specific with his promise to ensure Democrats vote "yes."

"I do think it would be helpful if the language were a little bit stronger," Collins told reporters.

But she also gave McConnell credit, saying the GOP leader "had moved to accommodate the concerns that have been raised" about needing a commitment on immigration.

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.) predicted McConnell will make a "firmer commitment when it seems like it will matter."

"I think if Mitch were a little firmer as to 'we are going to move to immigration. ... There will be a process where everybody will be heard,'" he said.

Graham suggested that Democrats go to Senate Minority Leader Charles Schumer Chuck SchumerVideo of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Graham signals support for confirming a Supreme Court nominee this year Pelosi orders Capitol flags at half-staff to honor Ginsburg MORE (D-N.Y.) and tell him that they will vote for the continuing resolution if McConnell will use more specific language.

McConnell has said he intends to take up an immigration bill if a larger deal can't be reached by Feb. 8.

But Democrats are quick to point to previous commitments to GOP Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (Ariz.) and Collins that did not come to fruition.

Flake, asked how Democrats could trust McConnell, noting that the GOP leader was making a "pretty high-profile promise."

Republican leaders, however, said Democrats have no reason to be distrustful.

"I think they ought to believe him because he's a trustworthy, honorable person. And I realize there's ... a trust deficit up here generally. But I think one of the first steps to regaining that trust is for the leader to make that commitment and follow through on it," said Senate Republican Whip John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (R-Texas).

Cornyn said Democrats would not get a more ironclad promise.

"No, I think that's all they're going to get," he said.

Peter Sullivan and Jordain Carney contributed.

Updated at 10:59 a.m.