Updated 6:13 p.m. | The Senate kicked off its long-awaited immigration debate Tuesday not with the flurry of bipartisan cooperation that some lawmakers had hoped for, but with a thud.

Before a single vote was cast to amend the shell bill serving as the vehicle for a potential deal, leaders of both parties were at an impasse over how to structure the debate, which is aimed at reaching a compromise to protect 690,000 “Dreamers” from deportation and meeting President Donald Trump’s immigration enforcement and border security goals.

In the Senate, process is just as important as substance at this stage since the chamber operates on unanimous consent.

Majority Leader Mitch McConnell proposed around noon Tuesday to hold votes later in the day, one on an amendment by Pennsylvania Republican Patrick J. Toomey that would target so-called sanctuary cities, and another on an amendment of the Democrats’ choosing.

“With their consent, we can start the debate,” McConnell said.

Watch: Senate Leaders Discuss Immigration Debate Progress So Far

But Minority Leader Charles E. Schumer objected because Toomey’s amendment would not help Dreamers enrolled in the expiring Deferred Action for Childhood Arrivals, or DACA, program or address border security, Trump’s top priority.

“To begin this debate as the Republican leader suggests would be getting off on the wrong foot,” he said.

Schumer instead asked McConnell to hold votes on two other amendments, a bipartisan proposal by Delaware Democrat Chris Coons and Arizona Republican John McCain, and a GOP proposal by Judiciary Chairman Charles E. Grassley of Iowa that has the president’s blessing.

Last chance?

Trump took to Twitter to reinforce McConnell.

“Republicans want to make a deal and Democrats say they want to make a deal. Wouldn’t it be great if we could finally, after so many years, solve the DACA puzzle?” he tweeted.

Negotiations on DACA have begun. Republicans want to make a deal and Democrats say they want to make a deal. Wouldn’t it be great if we could finally, after so many years, solve the DACA puzzle. This will be our last chance, there will never be another opportunity! March 5th.

— Donald J. Trump (@realDonaldTrump) February 13, 2018

Trump said that after March 5, the day on which he plans to begin winding down the Obama-era DACA program, “there will never be another opportunity” to protect Dreamers.

But federal court orders, including one issued Tuesday, are largely blocking him from ending the immigration program, making the deadline somewhat flexible. 

Still, senators don’t have much time to act. McConnell raised the stakes further by proclaiming that if the Senate did not pass immigration legislation this week, it is unlikely to get another shot. Congress is scheduled to be on break next week for the Presidents Day recess.

“The sooner we get started, the better, because we’ll need to wrap this up this week,” the majority leader told reporters. “If there are 60 votes for any of these proposals, we should be able to discover that in the next few days.”

Proposals filed

So far, Republicans have filed about a dozen amendments to the shell bill, though most of them are unrelated to the debate over Dreamers.

In addition to the Toomey amendment, which would authorize the Homeland Security Department to withhold grant money from sanctuary jurisdictions, Republicans are floating proposals to establish English as the national language, authorize longer detention periods for certain immigrants, and add a question about citizenship to the census.

Watch: Schumer Talks Immigration Debate ‘Gravity,’ and Senate’s ‘Special Obligation’

“We certainly had ample time to prepare,” McConnell said, chiding Democrats over their apparent lack of proposals. “The clock is ticking but the debate has yet to begin.”

So far, Democrats have only filed the McCain-Coons agreement.

It’s unclear whether other proposals may surface. A bipartisan group known as the Common Sense Coalition is still seeking to reach consensus on a proposal that might garner the 60 votes needed for passage, but members are unsure if anything will come together.

Arizona GOP Sen. Jeff Flake, a staunch advocate for Dreamers, is floating a proposal that he says addresses all of Trump’s priorities, including so-called chain migration, the process by which immigrants sponsor their family members for green cards and eventual citizenship.

Trump wants to bar immigrants from sponsoring anyone except their spouses and minor children, which would amount to sharp cuts in current immigration levels opposed by nearly all Democrats and some Republicans, including Flake. His proposal would instead apply those limits only to Dreamers, not a larger pool of immigrants.

Courts step in

The legislative debate over the Dreamers comes as legal moves challenging Trump’s decision to rescind DACA pick up steam. A second federal judge on Tuesday issued a nationwide injunction blocking him from ending DACA.

The ruling by U.S. District Court Judge Nicholas G. Garaufis in Brooklyn means the Trump administration must process applications for renewed and initial DACA protections as long as litigation is ongoing. The legal challenge to Trump’s order winding down the program was brought by Democratic attorneys general and immigration advocates.

A federal judge in California issued a similar order in January, complicating congressional efforts to provide Dreamers with some sort of legal status.

Garaufis said that while Trump undoubtedly has the power to end DACA, his stated reasons for doing so — that it is unconstitutional and indefensible — were “arbitrary and capricious.”

The administration appealed the January ruling by U.S. District Judge William Alsup to the Supreme Court and, in a rare step, asked the justices to overturn the lower court order quickly. But the Justice Department did not ask the court to immediately halt the order by Alsup.

The government told the Supreme Court that a primary purpose of the orderly wind-down of the DACA policy was “to avoid the disruptive effects on all parties of abrupt shifts” in immigration enforcement.

The Supreme Court has put the government’s appeal of the Alsup ruling on its closed-door conference agenda for Friday and will announce later whether to intervene or let the government’s appeal play out first in the U.S. Court of Appeals for the 9th Circuit.

Alsup and Garaufis are both Bill Clinton appointees.

Todd Ruger contributed to this report.