I appreciate your advice about how to handle this - we'll decide the order in which we offer our [amendments], and I'm not trying to dictate to them the order which they may offer their [amendments] ...
Durbin, who has long championed Dreamers and is sponsor of a bipartisan bill to give them legal authority to work and live in the United States and become citizens, invoked the story of Olympic gold medalist Chloe Kim as evidence of the importance of immigration.
Trump himself is expected to play an influential - but perhaps destabilizing - role in the process. But there's also the issue of McConnell undercutting time by propping up measures that will go nowhere with Democrats.
"This proposal has my support and during this week of fair debate I believe it deserves support of every senator who's ready to move beyond making points and actually making a law", Mr McConnell, said in a speech on the Senate floor.
The Secure and Succeed Act offers a 10- to 12-year path to citizenship for Dreamers.
Over the weekend, Trump also tweeted of "creating a safe, modern and lawful immigration system" that also includes more border security, ending diversity lottery program and family-based legal migration.
They proposed $25 billion to build a border wall, an end to the catch-and-release policies that free illegal immigrants into the interior of the USA, new faster deportations for visitors who overstay their permits, and permanently authorizing the E-Verify system that some businesses use to check their workers' legal status.
"They better get it done quick because it's this week or not at all", said Senate Majority Whip John Cornyn.
Cotton also suggested Trump was done negotiating.
"The President's framework is not an opening bid in negotiation".
Trump surprised many of his core supporters when he offered liberal Democrats an amnesty plan for an estimated 1.8 million illegal aliens in exchange for funding a border wall and changes to legal immigration laws that are popular with immigration watchdog groups.
"We are continuing to really talk turkey, legislative language etc", said Democrat Sen.
The bourbon Schumer presented, Widow Jane, is actually distilled in Kentucky, but purchased barreled young and then taken to NY to age.
"Something passed the Senate in 2013, we've spent three months talking to the Democrats about this, there's no reason in the world why, if there is a core 60 votes to support something, we can't achieve it in the next few days".
"No easy task", he added.
"We have other things to do", McConnell, a Kentucky Republican, told reporters Tuesday.
The debate comes after months of gridlock and procrastination on the issue in Congress. Last September, Mr Trump announced he would terminate the program on March 5. The program has granted temporary legal protections to hundreds of thousands of "dreamers".
The Cotton bill could meet stiff resistance.
Democrats and some Republicans have opposed Trump's hardline stance, especially the restriction of family-based immigration to spouses and children, and massive funding for the border wall. "That's why I was disappointed that the majority leader attempted to start voting today with an amendment that does absolutely nothing to address DACA, does absolutely nothing to address border security". The plan carries a significant political risk that none of the ideas will have enough votes to pass, leaving Congress unable to fulfill its pledge to protect the roughly 700,000 people enrolled in the Deferred Action for Childhood Arrivals program. It does not mention anything about skilled workers' immigration.