WASHINGTON (AP) - The Senate voted Tuesday to jump-start a stalled immigration measure to legalize millions of unlawful immigrants in the United States.

President George W. Bush said the bill offered a "historic opportunity for Congress to act," and appeared optimistic about its passage by week's end.

The pivotal procedural vote was 64-35 to revive the divisive legislation. It still faces formidable obstacles in the Senate, including bitter opposition by conservatives in Bush's Republican Party and attempts by some waverers in both parties to revise its key elements.

Supporters needed 60 votes to scale procedural hurdles and return to the bill. A similar test-vote earlier this month found just 45 supporters, only seven of them Republicans. This time, 24 Republicans joined 39 Democrats and independent Sen. Joseph I. Lieberman to move ahead with the bill. Opposing the move were 25 Republicans, nine Democrats and independent Sen. Bernard Sanders.

Democratic Sen. Edward M. Kennedy, an architect of the bill, said he was proud of the vote, "a major step forward for our national security, for our economy and for our humanity."

"We did the right thing today because we know the American people sent us here to act on our most urgent problems. We know they will not stand for small political factions getting in the way," Kennedy said in a statement after the vote.

Tuesday's outcome was far from conclusive, however. The measure still must overcome another make-or-break vote as early as Thursday that will also require the backing of 60 senators, and there is no guarantee that it will ultimately attract even the simple majority it needs to pass.

The Senate was preparing to begin voting as early as Tuesday afternoon on some two dozen amendments to the legislation that have the potential to either sap its support or draw new backers.

Republicans and Democrats alike are deeply conflicted over the measure, which also creates a temporary worker program, strengthens U.S. border security and institutes a new system for weeding out illegal immigrants from workplaces.

Bush has mounted an unusually personal effort to defuse Republican opposition to the bill, appearing at a Senate party lunch earlier this month and dispatching two Cabinet secretaries to take up near-constant residence on Capitol Hill to push the compromise.

He called the measure a deal worthy of support. "In a good piece of legislation like this, and a difficult piece of legislation like this, one side doesn't get everything they want," he told business leaders and representatives of religious, Hispanic and agricultural communities earlier Tuesday. "It's a careful compromise."

Sen. Edward M. Kennedy, a Democrat and an architect of the measure, sounded a similar tone. "This may not be perfect, but it is the best opportunity we have to do something significant and substantial, and I believe that the bill is good," he said.

Still, after a chaotic several weeks in which the measure survived several near-death experiences, it remained buffeted by intraparty squabbles in both parties.

As senators prepared for Tuesday morning's vote, Republicans met privately in the House of Representatives to work out how best to register their opposition through a party resolution. The measure never saw a vote for procedural reasons, but an attempt to kill it failed overwhelmingly, signaling deep Republican skepticism.

"It's clear there's a large number of the House Republicans who have serious concerns with the Senate bill," said Rep. John Boehner, leader of the House Republican minority.

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