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

President Bush said the bill offered a “historic opportunity for Congress to act,” and appeared optimistic about its passage by week’s end.

The pivotal test-vote was 64-35 to revive the divisive legislation. It still faces formidable obstacles in the Senate, including bitter opposition by GOP conservatives 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 of Connecticut, to back moving ahead with the bill. Opposing the move were 25 Republicans, nine Democrats and independent Sen. Bernard Sanders of Vermont.

Sen. Edward M. Kennedy, D-Mass., an architect of the bill, said he was proud of the vote, calling it “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 following 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 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 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.”

The vote suggested that key senators and White House officials had succeeded _ at least for now _ in bargaining with skeptical lawmakers for a second chance to pass the bill. Several senators who have been promised votes on their amendments, including Sens. Kit Bond, R-Mo., Barbara Boxer, D-Calif., Norm Coleman, R-Minn., Pete Domenici, R-N.M., John Ensign, R-Nev., and Jim Webb, D-Va., switched their votes to support moving ahead with the measure.

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

As senators were preparing for the showdown vote Tuesday morning, House Republicans meeting privately on the other side of the Capitol were plotting 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 GOP 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, R-Ohio, the minority leader.

Several of the Republican amendments slated for upcoming Senate votes would make the bill tougher on unlawful immigrants, while those by Democrats would make it easier on those seeking to immigrate legally based solely on family ties.

Particularly worrisome to supporters, including the Bush administration, is a bipartisan amendment by Sens. Charles Grassley, R-Iowa, Barack Obama, D-Ill., and Max Baucus, D-Mont., that would change the bill’s new program for weeding out illegal employees from U.S. workplaces.