As the Senate voted 97-1 on Monday to move past the first procedural hurdle in the way of an immigration debate on the Senate floor, Republican Senators made clear they were not interested in a lengthy debate on DACA, as they pressed Democrats to simply accept a plan offered by President Donald Trump on illegal immigrant Dreamers, arguing no other measure would get through the U.S. House and garner the President's support.

"The President's framework is not an opening bid in negotiations, it is a best and final offer," said Sen. Tom Cotton (R-AR), as a group of GOP Senators - backed by their Senate leadership - argued for a quick resolution on DACA.

"This plan is the only Senate plan that has any possibility of passing the House of Representatives and becoming law," said Sen. Charles Grassley (R-IA), as Republicans pressed ahead with an immigration plan that mirrors the four points backed by President Trump, labeling it a 'reasonable compromise.'

On Tuesday morning, the President turned up the heat another notch - casting the next few weeks as a last opportunity for Democrats to get a deal to help as many as 1.8 million illegal immigrants - brought here by their parents - to stay in the country.

"This will be our last chance, there will never be another opportunity!" Mr. Trump tweeted.

The GOP plan unveiled on the Senate floor Monday tracks what the President has said he will accept, 1) $25 billion for border security, 2) an end to the diversity visa lottery program, 3) new limits on family migration for those who gain citizenship, and 4) a 12 year path to citizenship for certain illegal immigrant "Dreamers" and DACA recipients.

"There's no reason that reasonable people can't get behind this," said Sen. David Perdue (R-GA), who argued there must be more than a resolution for just Dreamers.

"This plan to fix our immigration system will ensure we aren’t back here in just a few years," Perdue said.

But the push for a quick vote this week on that GOP plan was not what had been advertised to Democrats, who arrived on the Senate floor Monday afternoon believing they were ready for a rare freewheeling debate on the Senate floor, where no one was sure of the outcome.

"It's going to be a robust debate, and it could produce the best of what the Senate can produce, a bipartisan agreement, which it will have to be in order to get to 60 votes," said Sen. Bill Nelson (D-FL), as both sides know they need votes from the other party in order to come up with a plan that can pass the Senate.

Democrats continue to complain that weeks of negotiations on immigration have barely moved the needle on the DACA debate, as they argue White House hardliners are preventing the President from cutting a deal.

There has been some talk of a one-for-one offer - Democrats would get Dreamer protections in exchange for the President's $25 billion in border security money, as Democrats aren't very interested in the President's other immigration ideas.

But when the Senate adjourned on Monday evening, it became clear that Republicans were not looking for an extensive floor debate featuring votes on a variety of amendments and proposals.

Instead, top GOP Senators made clear they want to finish work on DACA as soon as this week, as Republicans said no plan from Democrats would ever make it to the President's desk.

"I have a huge problem with producing a result here in the Senate that has no chance of going to the President's desk and becoming law," said Sen. Thom Tillis (R-NC), who has worked with fellow Republicans to forge a plan based along the lines of what President Trump has said that he would support.

"The ultimate is whether the President will sign it or not," said Grassley.