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A hard-fought immigration reform bill will return to the Senate Monday after top lawmakers came to agreement over how to proceed on amendments to the bill and which senators will be on the team to broker a deal over differences between the House and Senate.

The announcement brokered by Senate Majority Leader Bill Frist of Tennessee and Senate Minority Leader Harry Reid of Nevada came Thursday, nearly four weeks to the day after negotiations crumbled in the Senate over how to deal with the estimated 12 million illegal immigrants currently living in the United States. Lawmakers hope the legislation can be finished before Memorial Day.

It appears that the plan that was last under consideration in the Senate — which included a controversial guest worker program — will largely proceed unchanged. It will be up to the House and Senate negotiators to come up with a plan to which they both can agree.

Frist, speaking with FOX News, said lawmakers will focus on securing the border and trying to create a temporary worker program.

"It's hard, it's challenging. We've got to secure that border. ... A strong temporary worker program again has to be defined," Frist said. "The focus will be on ... the 12 million people who are here illegally. They broke the law. We're a nation of laws."

Thursday's breakthrough did not include an agreement on the number of amendments that would be offered or considered, but Reid spokesman Jim Manley said both leaders have agreed to "a considerable number." A senior aide to Frist told FOX News that leaders have agreed to process the amendements "fairly, one at a time, with reasonable time agreement, and then votes."

Sen. Edward Kennedy, D-Mass., a key negotiator on the compromise bill, applauded the agreement.

"I think the most important judgment and decision that can be made on immigration reform is to get presidential leadership," Kennedy said. "With his involvement, his participation and his leadership, this country will make progress and we will have a valuable piece of legislation."

Kennedy added that he believed the measures would "fix our broken borders, strengthen our national security, mean new opportunities and new hope for people that want to provide for their families and want to become Americans after they pay penalties and earn their citizenship and go to the end of the line."

The White House offered praise of the announcement.

"We congratulate the Senate on reaching agreement and we look forward to passage of a bill prior to Memorial Day," said Dana Perino, deputy White House press secretary.

Amendments to the Senate bill could still be a point of friction. Republicans, including Frist and President Bush, accused Reid of blocking debate on all but a handful of amendments to the bill, which they said was why the compromise fell apart last month. Democrats said they wanted to protect the bill from being watered down. The conference team also had been a source of partisan bickering.

But Republicans haven't come out of the debate unscathed. Moderate Republicans have faced opposition from the conservative branch of the party over the compromise, who contend that any guest worker proposal amounts to amnesty, or favorable treatment of illegal immigrants over those trying to enter the country legally.

Frist said 40 percent of illegal immigrants have lived in the United States longer than 10 years, a point lawmakers will contend with in their work.

"What we will do is define that 12 million [people], treat them fairly ... with compassion, but also not give them an automatic path to citizenship that in any way gives them a leg up, or amnesty, with regard to other people who are waiting to come in this country" legally, Frist said.

The House bill, ushered through by Republicans, does not contain a guest-worker provision, and was the target of dozens of protests around the country in recent weeks, drawing hundreds of thousands of immigrants and their supporters to the streets.

Manley said a major breakthrough in the negotiations was on the makeup of the so-called conference committee of House and Senate members who will hash out the differences between the two chambers. The Senate side will include 26 conferees; 14 Republicans and 12 Democrats.

The Republican members will be comprised of the seven most senior members of the Senate Judiciary Committee and seven others chosen by Republican leadership. The Democrat side will be comprised of the five most senior members of the Senate Judiciary Committee, plus seven others picked by top Democrats.

The House negotiation team has not been finalized.

Sen. John Cornyn, R-Texas, who has opposed the compromise, is one of the lawmakers named to the conference committee.

"My focus will remain on fighting for stronger border security, interior enforcement, employer verification and reform that brings the current illegal population into compliance with the law," Cornyn said in a statement released by his office. "The differences between the House and Senate bills are significant, and the solutions will be difficult. But it's important to have border state senators on this committee to help craft a final bill that meets our national security and economic needs."

Speaking on the Senate floor Thursday, Reid admitted he "didn't get everything that I wanted" in the agreement, but said Frist didn't either. Reaching the agreement is "not easy with the political atmosphere," Reid said.

Presidential and midyear politics have been a subtext to the immigration debate. Frist and Arizona Sen. John McCain, one of the architects of the legalization proposal, are prominent potential candidates for the 2008 GOP presidential nomination.

The compromise bill, forwarded by Sens. Chuck Hagel, R-Neb., and Mel Martinez, R-Fla., builds on legislation approved by the Senate Judiciary Committee 12-6, with four Republicans voting with Democrats to approve the measure.

That measure absorbed a bill drafted by McCain and Kennedy. Their bill called for allowing illegal immigrants to work toward becoming legal permanent residents and later citizens.

Bush pushed for speedier progress on the bill during a meeting with a bipartisan group of senators last month, renewing his call for allowing illegal immigrants a path to citizenship.

FOX News' Trish Turner and The Associated Press contributed to this report.