WASHINGTON  — A high-stakes Senate debate over immigration got off to a halting start Tuesday, with Republican and Democratic leaders immediately at loggerheads over how to move forward and President Donald Trump warning this was the "last chance" to extend protections to "Dreamer" immigrants.

Trump issued the warning in a morning tweet as the Senate opened what was billed as an unusual and open-ended debate on a host of immigration issues. Democrats had pushed for the debate, hopeful they might be able to craft a piece of legislation in real time on the Senate floor — or at least force Republicans on the record on some difficult issues.

But the experiment in legislating didn't go very far.

Senate Majority Leader Mitch McConnell, R-Ky., began the process by throwing his weight behind legislation based on the president's priorities.

To kick the debate off, McConnell proposed allowing Republicans to bring up an amendment targeting cities that don't fully cooperate with federal immigration authorities, so-called "sanctuary cities." Then, Democrats would bring up legislation of their choosing. Amendments gaining 60 votes would become part of the broader immigration bill.

The Senate's top Democrat, Chuck Schumer of New York, quickly objected.

"To begin the debate as the Republican leader suggests would be getting off on the wrong foot," Schumer said. "Very partisan."

Schumer wants McConnell to bring up legislation that incorporates President Donald Trump's priorities and a second, much narrower bill from Sens. John McCain, R-Ariz., and Chris Coons, D-Del.

His reasoning: The legislation should address the population of young immigrants that lawmakers from both parties say they want to help, rather than deal with side issues such as punishing sanctuary cities.

McConnell replied: "I'm not trying to dictate to them what they offer. They shouldn't be trying to dictate to us what we offer. We ought to just get started."

The disagreement pushed any immigration-related votes into Wednesday. That gives a group of moderate lawmakers more time to come up with a package that could generate 60 votes in the Senate.

"Until we reach an end there, I still hope that's the vehicle," said Sen. Jeff Flake, R-Ariz., one of the group's key participants.

Exiting the Senate floor Tuesday evening, Sen. Dick Durbin, D-Ill., said "things change by the hour" on immigration, but he felt better as the day went on about the prospects of getting a bill passed. He said lawmakers are meeting privately in search of a compromise.

One GOP proposal based on principles dictated by the White House would pave a path to citizenship for up to 1.8 million young "Dreamer" immigrants in the U.S., a lure for Democrats that many Republicans oppose.

Trump also wants $25 billion for Trump's border wall with Mexico and other security measures, as well as curbs on legal immigration — a must for many Republicans.

"This proposal has my support, and during this week of fair debate, I believe it deserves the support of every senator who's ready to move beyond making points and actually making a law," McConnell said.

McConnell and other GOP supporters describe the measure as the Senate's best shot of passing a bill that the president will sign, but many Democrats consider some of the proposals, including limiting the relatives that legal immigrants can bring to the U.S., to be non-starters.

Schumer expressed opposition to Trump's sweeping approach, pushing for a more narrow focus.

"Helping the Dreamers become Americans and protecting our borders. That should be the focus of all our energies," Schumer said.

Trump's overall immigration plan, opposed by many Democrats, stands little chance of prevailing because any measure will need 60 votes. That means proposals will need substantial bipartisan support since the GOP majority is 51-49, and Sen. John McCain, R-Ariz., has been absent in recent weeks battling cancer.

Still, many Republicans insist that legislation incorporating Trump's priorities is a compromise because it gives up to 1.8 million young immigrants a pathway to citizenship.

"The president's framework is not an opening bid in negotiations. It is a best and final offer," said Sen. Tom Cotton, R-Ark.