WASHINGTON – Senate leaders agreed Monday that they would wait until June to take final action on a bipartisan plan to give millions of unlawful immigrants legal status.

The measure, which also tightens border security and workplace enforcement measures, unites a group of influential liberals, centrists and conservatives and has White House backing, but it has drawn criticism from across the political spectrum. In a nod to that opposition, Senate leaders won’t seek to complete it before a hoped-for Memorial Day deadline.

“It would be to the best interests of the Senate … that we not try to finish this bill this week,” said Senate Majority Leader Harry Reid, D-Nev., as the chamber began debate on the volatile issue. “I think we could, but I’m afraid the conclusion wouldn’t be anything that anyone wanted.”

The bipartisan compromise cleared its first hurdle Monday with a bipartisan Senate vote to begin debate on a separate immigration measure. Still, it faces significant obstacles as lawmakers seek dozens of modifications to its key elements.

Republicans want to make the bill tougher on the nation’s estimated 12 million illegal immigrants. Democrats want to change a new temporary worker program and reorder priorities in a merit-based system for future immigration that weights employability over family ties.

The unlikely coalition that brokered the deal, led by Sens. Edward M. Kennedy, D-Mass., and Jon Kyl, R-Ariz., is plotting to protect the agreement from “deal-breaker” changes that would sap its support. The group will hold daily meetings starting Tuesday to determine whether proposed revisions would sink what they are calling their “grand bargain.”

“We have to try our very best to work together to get something that will actually pass,” Kyl said.

Among the first changes to be debated will be a proposal by Sen. Jeff Bingaman, D-N.M., to shrink the temporary worker program created by the compromise plan. Some lawmakers in both parties consider the initiative, which would provide at least 400,000 guest worker visas annually, too large.

Others charge it’s impractical and unfair to immigrants, because it would allow them to stay only temporarily in the U.S. without guaranteeing them a chance to gain legal status.

“We must not create a law that guarantees a permanent underclass, people who are here to work in low-wage, low-skilled jobs but do not have the chance to put down roots or benefit from the opportunities of American citizenship,” Reid said.

Reid called the measure a “starting point,” but said he had reservations about it.

Conservative critics denounced the proposal’s quick granting of legal status to millions of unlawful immigrants.

Sen. Jeff Sessions, R-Ala., said the measure’s so-called “point system” doesn’t do enough to guarantee that future immigration will serve the country’s economic needs.

“I’m nervous about this thing,” said Sessions, who voted not to go forward with the debate. He called the point scheme “bait” to get conservatives to embrace the measure, and accused Republicans of compromising too much on an outline drafted by the White House in late March to attract GOP support.

“I’m disappointed – almost heartbroken – because we made some progress toward getting to this new framework, but the political wheeling and dealing and compromising and splitting the baby has resulted in a circumstance that, you know, we just didn’t get far enough,” Sessions said.

Sen. Kay Bailey Hutchison, R-Texas, who also opposed opening debate, announced she would seek to alter the bill to mandate that illegal immigrants go back to their home countries before gaining legal status.

Under the proposal, that requirement only applies to heads of households seeking green cards and a path to citizenship.

Others here unlawfully could obtain visas to live and work in the U.S. indefinitely without returning home.

Kennedy, called the plan “strong, realistic and fair.”

“For each of us who crafted it, there are elements that we strongly support and elements we believe could be improved. No one believes this is a perfect bill,” Kennedy said.

The White House has begun an active lobbying effort to drum up support for the measure, especially among Republicans who voted against an immigration overhaul last year.

President Bush is still hoping to sign the bill by summer’s end, said Tony Fratto, a White House spokesman.

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