The Senate's comprehensive immigration bill, bolstered by new language meant to quiet accusations the bill delivers amnesty, passed a crucial procedural test Tuesday that vastly improves but does not guarantee its chance of passage.

The Senate voted 64-35 to bring the bill back to the Senate floor from the legislative limbo to which it had had been exiled earlier this month, when it appeared to die after a bipartisan filibuster.

Bill supporters needed 60 votes to bring the bill back to the floor for debate. Had that threshold been missed, it's likely the bill would have been dead for the remainder of the 110th Congress.

Opponents of the Senate immigration bill pushed hard for its defeat on the procedural motion but fell five votes short, precisely the number they were behind on Monday.

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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.

Organizations like Numbers USA, a potent grassroots organization that has led mass e-mail, phone and fax protests against the bill, targeted GOP Sens. Kit Bond of Missouri, John Ensign of Nevada and Thad Cochran of Mississippi. Bond and Ensign voted to bring the bill back before the Senate.

Indeed, a poll released Monday by Rasmussen Reports shows only 22 percent of Americans support the bill now on the floor. Republican grassroots opposition organizations have mobilized to block the cloture vote.

Stephen Elliott, president of one such group, Grassfire.org, said Monday that a "yes" vote for cloture on the bill supported by the likes of President Bush and Democratic Sen. Ted Kennedy "is a 'yes' vote for amnesty. Any senator who votes 'yes' on tomorrow's cloture motion to proceed with this bill will forever be labeled an amnesty senator — even if that senator later votes against final passage."

The Senate will now consider a series of 24 amendments to the bill during the remainder of the week while the White House and the bipartisan Senate leadership lobby hard for its approval by Friday and the start of a week-long Fourth of July congressional recess.

Tuesday's vote came just a few hours after President Bush pumped up the rhetoric in support of the legislation.

"The immigration system needs reform," Bush said at a briefing on immigration reform in the Eisenhower Executive Office Building.

"The status quo is unacceptable. ... I view this as a historic opportunity to act, for Congress to replace a system that is not working with one that we believe will work a lot better," he said.

The president also thanked administration officials who have been lobbying hard to persuade Republicans to support one of the president's top domestic priorities. Commerce Secretary Carlos Gutierrez and Homeland Security Secretary Michael Chertoff have led the negotiations.

Bush fought off criticism that the bill gives amnesty to lawbreakers, though in a oratorical flub the president seemed to suggest the bill does just that.

"Amnesty means that you've got to pay a price for having being here illegally and this bill does that. But it also recognizes in our nation's interest to bring people out of the shadows," Bush said. "There's got to be a way forward that recognizes there is a penalty for being here illegally, on the other hand, that recognizes that each person has worth and dignity."

Shortly after the president's remarks, White House Press Secretary Tony Snow issued an unusual statement to correct his boss.

"Earlier today, in speaking about comprehensive immigration reform, President Bush misspoke," Snow said.

"This has been construed as an assertion that the comprehensive immigration reform legislation before the Senate offers amnesty to immigrants who came here illegally," he said. "That is the exact opposite of the president's long-held and often-stated position."

Despite the confusion, the bill is vulnerable to charges of amnesty because of the Z-visa provision that opponents assert will it very hard for the federal government to deport anyone in possession of legal status. The visa grants instant probationary legal status to any illegal immigrant living or working in America now.

"I know people think that the draft language is a perfect draft and believe it should somehow attain its own mythological status, but this is pretty straightforward. If an alien applies, he or she gets legal status, full travel and work authorization no later than the next day," said Sen. John Cornyn, R-Texas, an opponent of the bill.

The Z-visa provides indefinite legal status and is the first step to obtaining a green card and citizenship — an 8- to 13-year process that includes the payment of fines, processing fees, criminal background checks and representations that applicants attempted to learn English.

A last-minute change in the treatment of applicants for the all-important new visa may defuse some of the opposition.

Under the original Senate bill, only the head of a household would have to return to his or her country of origin to apply for a green card. The bill did not require any Z-visa applicants to return to their country of origin, meaning if an illegal immigrant didn't want a green card, they could re-apply for the four-year Z-visas indefinitely. Under the new language, all heads of household who seek a Z-visa will have to return to their country of origin and apply.

Despite this alteration, the Senate bill still has a long way to go before final passage in the Senate. It also faces proactive Republican hostility in the House.

A Short List of Amendments

A handful of the 24 amendments are causing heartburn for some bill supporters. Aides to supporters say the list was chosen with cloture in mind.

"Get an amendment on the list, give me cloture," one aide characterized the effort bluntly.

Senate Majority Leader Harry Reid, D-Nev., will employ a rarely-used tactic to freeze out all other amendments. Called a "clay pigeon," the move allows Reid to shoot open one large amendment into a finite list of smaller amendments when the debate begins. Aides say any problematic amendments could face a "tabling" motion — requiring only 51 votes to kill the amendment.

Reid noted that the procedure was unusual, but necessary to block a Republican filibuster. He added that the move has the support of GOP leader Sen. Mitch McConnell of Kentucky and the White House.

Already, the battle lines appear to be drawn for a major fight on a family-related amendment authored by Cuban-American Sen. Bob Menendez, D-N.J., though some signs point to a possible compromise. Under Menendez's amendment, family members would get 10 extra points toward getting a green card in a newly-created 100-point evaluation system, with five more points going for those immigrants in line for a green card as of Jan. 1, 2007.

GOP members of the "grand bargain," as the Senate compromise bill is known, chafe at this possibility, as the new point system is designed to limit the number of family members coming into the U.S. to spouses and minor children — thus ending what Republicans call "chain migration" — and turn the focus instead on skills and education.

Sen. Mel Martinez, R-Fla., a bill co-sponsor, said a compromise is afoot on family migration, though details are unknown. "We are trying to do something with family reunification."

The newly-revised bill contains a sizeable increase in many of the components of border security added in the two weeks since the bill has been off the floor, including the recently announced $4.4 billion immediate infusion of funds, as well as the addition of a biometric national identification card.

Two thousand more border agents are to be "hired, trained, and reporting for duty," bringing the number of agents to 20,000; an additional 100 miles of vehicle barriers were just added, bringing that number to 300 miles; and 105 ground-based radar and camera towers are to be built, up from 70 just two weeks ago.

However, one Republican leadership aide told FOX News that the $4.4 billion is not nearly enough money to cover these substantial increases, warning against any guarantee that the provisions will be paid for down the road. "There's no way that's enough. So they'll have to appropriate more, and there's a big difference between authorizing and appropriating."

Another problematic amendment related to family is one by Democratic presidential candidate Sen. Chris Dodd of Connecticut. Under Dodd's amendment, the number of green cards for parents of U.S. citizens would more than double, from 40,000 to 90,000. Republicans, again, will oppose this, like the Menendez amendment, and it is likely, aides say, to be killed by the bipartisan compromise group, even though some chief negotiators, like Sen Ted Kennedy, D-Mass., support the idea.

Still another amendment designed to lure Republicans is one by Sen. Lindsey Graham of South Carolina, himself on the receiving end of conservative ire. Graham, part of the "grand compromise," would severely crack down on immigrants who overstay their visas, confronting those who cannot show some outstanding reason, like a health problem or a sick relative, with deportation and a life-time ban from the U.S.

Democrats will find this very difficult to accept, but one senior Republican aide said, "This one will be needed to get a number of Republicans on board."

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.

The amendment would free employers from a mandate to check the identities of all their employees and require them to verify only new workers and those the government has a reason to believe are illegal immigrants. It would allow employees to present any state-issued drivers license as proof of identity, rather than requiring the nationally standardized "REAL ID," which some states have not adopted.

White House Deputy Chief of Staff Joel Kaplan said the amendment is the only one the administration is actively lobbying against.

"We've got our work cut out for us," he said.

The Associated Press contributed to this report.