by Sheryl Gay Stolberg

WASHINGTON — With the fate of hundreds of thousands of young, unauthorized immigrants in the balance, the Senate on Monday began an open-ended debate on immigration — an exceedingly rare step that, in effect, will allow senators to attempt to build a bill from scratch on the Senate floor.

The highly unusual debate, expected to unfold throughout the week, will test whether a series of legislative concepts and proposals championed by President Donald Trump and a variety of Republicans and Democrats can garner 60 votes, the threshold for a measure to pass the Senate. No one has any idea how it will turn out.

“Whoever gets to 60 wins,” Sen. Mitch McConnell, the Republican leader, told reporters last week. “And it will be an opportunity for 1,000 flowers to bloom.”

The debate kicked off Monday evening with a procedural vote on an unrelated House-based measure that will serve as a shell for building an immigration bill. He has set aside this week for debate. By a vote of 97-1, with only Sen. Ted Cruz, R-Texas, dissenting, senators took the first step toward consideration of the underlying measure, as expected.

The push on immigration comes against the backdrop of a ticking clock, and months of congressional inaction.

About 700,000 young immigrants who were brought to the United States illegally as children are shielded from deportation under an Obama-era initiative known as the Deferred Action for Childhood Arrivals, or DACA. Another 1.1 million young immigrants are eligible for DACA but did not apply. But Trump suspended the initiative in September and gave lawmakers until March 5 to come up with a replacement that that would protect the young immigrants, known as Dreamers, after proposed legislation called the Development, Relief and Education for Alien Minors, or DREAM Act.

Liberal interest groups and immigration rights activists have mobilized to insist on legal status for the Dreamers without the concessions demanded by the president and immigration hard-liners: billions for a wall on the Mexican border, an even more aggressive crackdown on unauthorized immigrants and dramatic changes to the legal immigration system that would favor skilled immigrants over the family members of citizens and green-card holders.

“As the Senate is poised to start debate on the humanitarian crisis Donald Trump caused when he cruelly ended DACA, here’s what every sitting senator should remember: Americans want the DREAM Act — not cruel deals that go against basic American values,” said Corinne Ball, campaign director for MoveOn.org, a liberal activist group.

Conservatives and anti-immigration groups are just as vociferous.

“It was President Obama who created a cruel situation by making promises to a group of illegal aliens who he had no authority to promise what he gave them,” said Rosemary Jenks, the director of government relations for NumbersUSA, a group that advocates limiting immigration. “President Trump had a duty to rescind that policy, because the Constitution makes very clear that Congress, not the White House, sets the laws in this land.”

In such a polarized environment, there is a significant chance that the Senate will pass nothing by the end of the week — or that whatever measure the Senate does adopt will be thwarted by the House.

“We’re going to have something in the Senate that we haven’t had in a while,” Sen. Jeff Flake, R-Ariz., said Sunday on the NBC program “Meet the Press.” “It’s a real debate on an issue where we really don’t know what the outcome is going to be.”

Immigration is one of the most emotional, contentious issues in Washington. The last time Congress seriously considered immigration legislation was in 2013, when the Senate passed a comprehensive immigration overhaul with 68 votes. But that measure, which offered a path to citizenship for about 11 million immigrants in the United States illegally — including the Dreamers — was never taken up by the House.

Trump’s election, on a wave of anti-immigrant fervor, has made the current negotiations even more difficult, senators say. The negotiations are complicated by Republicans’ demands to pair any protection for DACA recipients with an increase in border security, and limits on legal immigration, and by conflicting pronouncements from Trump.

After telling lawmakers last month that he would sign whatever they sent him, Trump now insists that any proposal address what the White House is calling “four pillars”: protection for DACA recipients; an end to what Trump calls “chain migration,” in which legal immigrants can sponsor their family members; an end to the diversity visa lottery, which is aimed at bringing in immigrants from underrepresented countries; and full funding for the proposed border wall, estimated to cost $25 billion over 10 years.

The White House recently put forth its own proposal that meets those conditions; it would offer 1.8 million Dreamers a path to citizenship, in exchange for strict limits on legal immigration and the full $25 billion for the border wall. A number of Republican senators, led by Charles E. Grassley of Iowa, have drafted legislation that mirrors the White House plan, which will almost certainly be introduced as an amendment. McConnell said on Monday that he supported it.

The American people have “heard many of my colleagues across the aisle insist this issue requires swift action,” McConnell said. “Now is the time to back up the talk with the hard work of finding a workable solution. That means finding an agreement that can pass the Senate, pass the House and which the president will sign — not just making a point.”

Several other proposals are floating around Capitol Hill, but so far none has garnered the backing of the White House. A bipartisan group calling itself the Common Sense Coalition, led by Sens. Susan Collins, R-Maine, and Joe Manchin, D-W.Va., has been working on its own measure but has not released a plan.

That group is focused on a narrower bill than the president would like, one that would pair a path to citizenship for the Dreamers with funding for the border wall.

“The only way to achieve a solution to the DACA crisis is to keep it simple,” Sen. Bill Nelson, D-Fla., a member of the coalition, said on the Senate floor Monday.

But Sen. John Cornyn of Texas, the No. 2 Republican, said he could not support a bill that addresses only DACA and border security. “The president’s indicated he would not sign such a bill, so that really doesn’t meet my definition of success,” he said.

At the same time, the idea of an open-ended debate is so novel that many newer senators say they have never experienced one, and are scurrying to learn the rules.

“For a lot of us, we’re going to have to learn this process,” said Sen. Mike Rounds, R-S.D., who was elected in 2014.

Sen. Chris Coons, D-Del., marveled, “Been here seven years — I’ve never seen anything like it.”

Immigrant rights groups are nervous, and do not know quite what to expect. Frank Sharry, the executive director of America’s Voice, an immigrant rights group, put it this way: “This is going to be an uncertain, wild week.”