WASHINGTON -- Politics still might get in the way of a final agreement on a bipartisan immigration bill.

Now that labor and business have agreed on an immigrant temporary-worker program, a bipartisan group of eight senators say they’ve cleared every major policy hurdle and are ready to introduce the most dramatic overhaul to the U.S. immigration system in decades.

But first they have to write the bill, and that’s rarely an easy task.

After weeks of speculation that an agreement was in jeopardy amid stalled talks and public bickering between the U.S. Chamber of Commerce and the AFL-CIO, Senate staff members are working the plan into draft legislation.

The so-called “gang of eight” senators have worked out the major concepts, including placing the 11 million illegal immigrants who are in the country now on a path to citizenship, beefing up border security, establishing a nationwide system to verify the legal status of workers, punishing businesses that hire illegal immigrants and allowing more agricultural and highly skilled immigrant workers to stay in the country.

But they still may hit several stumbling blocks as broad concepts must be turned into specific details that can sustain legal scrutiny. A key aspect of the proposal, for example, is that the borders must be secure before newly legalized immigrants are put on a path to citizenship. The members must come up with a system to measure border security, and whether they think the borders already are secure enough depends on what side of the aisle they sit on.

The senators also are planning to rewrite the laws to give preference to future immigrants based on potential job skills, with less emphasis on family connections. The system would award points for an immigrant’s various characteristics, and it would place greater emphasis than the system does now on the immigrant’s ability to make long-term economic contributions.

Sen. Patrick Leahy, D-Vt., the chairman of the Senate Judiciary Committee, has agreed to consider the bill later this month, according to Sen. Charles Schumer, D-N.Y.

Schumer, Sen. Lindsey Graham, R-S.C., and other members of the gang of eight took to the airwaves Sunday to herald the historic agreement, announce plans to unveil the legislation next week and call on President Barack Obama to help them make their case to the public.

On Monday, Obama applauded the progress and promised to remain engaged. But he cautioned that the legislation has yet to be presented, Press Secretary Jay Carney said.

“We’re not celebrating prematurely,” Carney said. “We await the product.”

Indeed, one member of the bipartisan team, Sen. Marco Rubio, R-Fla., who’s frequently mentioned as a 2016 presidential contender, appeared to be distancing himself from his excited colleagues.

“Reports that the bipartisan group of eight senators have agreed on a legislative proposal are premature,” he said in a statement Sunday.

Rubio faces a dilemma. He’s a favorite of die-hard conservatives, who have a strong say in Republican politics. But if he has national ambitions, he also must show broad appeal, particularly to the center-right, and immigration might be a key part of such a strategy.

Some political observers questioned whether Rubio was trying to lay the groundwork for removing himself from the group, but analysts such as Lance deHaven-Smith said Rubio had too much to lose.

The political science professor at Florida State University described Rubio as acting like a “reluctant bride.”

Rubio can’t afford to lose Hispanic support by walking away from the agreement, deHaven said.

“But on the other hand, if he rushes to this with open arms and culminates the marriage with glee, he alienates the tea party. He’s going to the altar with his head down and shuffling,” the professor said.

The “gang of eight” senators began crafting ideas for an immigration overhaul after the November elections, in which Hispanics voted overwhelmingly for Obama over Republican Mitt Romney.

The agreed-on guest worker proposal initially would provide 20,000 visas. The numbers would increase later, based on market demands and unemployment numbers, but wouldn’t exceed 200,000 per year.

“With the agreement between business and labor, every major policy issue has been resolved on the gang of eight,” Schumer said Sunday on NBC. “Now everyone, we’ve all agreed that we’re not going to come to a final agreement until we see draft legislative language and we agree on that.”

The other senators in the group are Democrats Richard Durbin of Illinois, Robert Menendez of New Jersey and Michael Bennet of Colorado and Republicans Jeff Flake and John McCain, both of Arizona.

Lesley Clark contributed to this article.

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