A “skinny” version of immigration reform with language that's scaled back from President Trump's preferred bill is emerging as the only measure that could possibly win enough votes to pass the Senate, which was still struggling on Tuesday to find a consensus.

Republicans and Democrats said Tuesday that a plan that pairs legal protection for so-called "Dreamers" with significant border security funding might have the momentum to win 60 votes in the Senate.

Such a bill would exclude reforms sought by Trump to end chain migration and the visa lottery system, issues that have divided the two parties and have made it impossible to find agreement.

While that bill would only include two of Trump's four pillars, lawmakers said the truncated plan could provide the only viable pathway to an accord ahead of the March 5 deadline Trump has set for Congress to replace the Deferred Action for Childhood Arrivals program, or DACA.

“It might be a two-pillar bill instead of a four-pillar bill,” Sen. Lindsey Graham, R-S.C., said Tuesday after meeting with Republican lawmakers in a closed-door meeting.

Supporters of the idea are hoping it can unclog a Senate that stumbled out of the gate Tuesday, when Democrats twice blocked a Republican motion to open the immigration debate with a vote on legislation that would withhold some federal funding from so-called "sanctuary cities."

The stalling tactic will limit how much time Republicans and Democrats have to debate various immigration reform proposals this week. Republicans only set aside this week for floor work on immigration, which means the clock is ticking to find a proposal that can pass.

Graham acknowledged that the four-pillar proposal by the Trump administration, while divisive, is “a serious offer” that has moved the Republican party “a long way” on immigration.

It would provide a pathway to citizenship for 1.8 million young people who came to the United States illegally as children in exchange for $25 million in border security funding and new limits to chain migration. The proposal would also end the visa lottery system.

Senate Majority Leader Mitch McConnell, R-Ky., backs the Trump plan, which has been introduced in the Senate by Sens. Tom Cotton, R-Ark., and David Perdue, R-Ga., among others.

But Graham said he doubts the bill could win 60 votes because the vast majority of Democrats oppose it. The provision to limit chain migration, which Democrats call family reunification, is the main sticking point, Graham said.

Democrats oppose the GOP plan to limit chain migration to nuclear families, comprised of minor children and spouses.

“I’m for going to nuclear family for chain migration,” Graham said. “I just think you are not going to get that [in exchange for] the DACA population.”

Graham said the Trump four-pillar framework would also draw opposition from business groups who oppose new limits to legal immigration.

Many Democrats Tuesday also called for a limited immigration reform bill.

“We continue to believe a narrow proposal has the best chance of passing the Senate and the best chance of being signed into law,” Senate Minority Leader Chuck Schumer, D-N.Y., said Tuesday after meeting with party lawmakers privately.

Sen. John McCain, R-Ariz., and Chris Coons, D-Del., have written legislation that would provide a pathway to citizenship for 3.2 million illegal immigrants in exchange for less than $3 billion for border security.

Schumer threw his support behind the proposal Tuesday, but Republicans acknowledged that bill is too weak on border security to ever win over the GOP.

“I think people are looking for something a lot more robust,” said Sen. Bob Corker, R-Tenn.

Sen. Jeff Flake, R-Ariz., is also proposing a narrow bill in case the broader legislation cannot win 60 votes. Flake’s proposal would extend the DACA program for three years in exchange for border security funding.

It has no Democratic support yet and it’s not clear how many Republicans would back it.

Graham said votes for some form of the two-pillar bill could materialize if the broader proposals fail.

“The way you pass a bill like this is you take off the table what won’t work, and what is left is probably what you can get 60 votes for,” Graham said.

In the meantime, the Senate found itself stuck Tuesday, and it wasn't clear Wednesday would be any more productive.

On Tuesday, Democrats twice blocked a bill from Sen. Pat Toomey, R-Pa., to withhold certain federal funding from jurisdictions that refuse to cooperate with federal immigration officials. Democrats argued that bill had nothing to do with the outline Trump has put forward on immigration.

But McConnell said Republicans said Democrats were free to offer their own amendments and neither party should be blocking proposals.

A time limit will expire on the Democratic hold Wednesday morning, but they'll likely impose another 30-hour delay when McConnell calls up the Toomey bill, which could postpone action yet again.

“I’m not trying to dictate to them what they offer,” McConnell said. “They shouldn't be trying to dictate to us what we offer. Let it just get started. This is the way we used to do it, and I'm giving us an opportunity to try that again."