The so-called Gang of Eight's plan would provide a new class of worker visas for low-skilled workers, secure the border, crack down on employers, improve legal immigration and create a 13-year pathway to citizenship for the millions of illegal immigrants already here.
"With the agreement between business and labor, every major policy issue has been resolved," said Sen. Chuck Schumer, the New York Democrat who brokered the labor-business deal.
But that effort hasn't taken the form of a bill and the senators searching for a compromise haven't met about the potential breakthrough. They plan to introduce their framework when they return from recess the week of April 8 and move quickly to schedule a vote.
Sen. Jeff Flake, R-Ariz., said the hard part is done.
"That doesn't mean we've crossed every 'i' or dotted every 't,' or vice versa," Flake said.
(Read More: Our Massively One-Sided Immigration Debate)
But even as the final stages of talks begin, one member of the group urged colleagues not to get too far ahead of themselves. Just before lawmakers began appearing on Sunday shows to discuss the breakthrough, Sen. Marco Rubio warned he was not ready to lend his name—and political clout—to such a deal without hashing out the details.
"Reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature," said Rubio, a Florida Republican who is among the lawmakers working to write the legislation.
Rubio, a Cuban-American who is weighing a presidential bid in 2016, is a leading figure inside his party. Lawmakers will be closely watching any deal for his approval, and his skepticism about the process did little to encourage optimism.
Rubio, who is the group's emissary to conservatives, called the agreement "a starting point" but noted 92 senators from 43 states haven't yet been involved in the process.
That's where figures such as Rubio and assistant Democratic leader Dick Durbin of Illinois come in. Both will be able to give political cover to—or coax —members of their party who were not involved in drafting this agreement that could allow an estimated 11 million illegal immigrants to earn U.S. citizenship.
"As to the 11 million, they'll have a pathway to citizenship, but it will be earned, it will be long, and it will be hard, and I think it is fair," Graham said.
A week ago, such a compromise seemed impossible.
Then the pro-business U.S. Chamber of Commerce and the AFL-CIO labor coalition reached its deal late Friday to allow tens of thousands of low-skilled workers into the country to fill jobs in construction, restaurants and hotels.
Schumer negotiated the deal between Chamber of Commerce head Tom Donohue and AFL-CIO president Richard Trumka during a late Friday phone call. Under the compromise, the government would create a new "W" visa for low-skilled workers, who would earn the same wages paid to Americans or the prevailing wages for the industry they're working in, whichever is higher. The Labor Department would determine prevailing wage based on customary rates in specific localities, so it would vary from city to city.
The detente between the powerful business lobbying group and the nation's leading labor federation still needs senators' approval, including a nod from Sen. John McCain, the Arizona Republican whose previous efforts came up short. He has returned to the negotiating table yet again.
The immigration debate already has President Barack Obama's attention.
"This is a legacy item for him," said David Axelrod, a longtime political confidant of Obama. "There is no doubt in my mind that he wants to pass comprehensive immigration reform."
Graham was interviewed Sunday on CNN's "State of the Union." Schumer, Flake and Axelrod appeared on NBC's "Meet the Press."