The legislation, backed by the White House and most Democrats, must clear at least two more 60-vote tests this week -- allowing a final vote and a budgetary point of order -- and it faces uncertainty in the House, where conservatives on Tuesday said they would try to block it.
"I'm optimistic, but it could fall apart at any time," said Sen. Dianne Feinstein, D-Calif.
Twenty-four Republicans joined most Democrats to approve the procedural motion. The next step, according to leadership aides, is for Majority Leader Harry Reid, D-Nev., to file an omnibus amendment containing 24 provisions that leaders have agreed will receive individual votes before final passage.
Among the last-minute changes in the list is a proposal by Majority Whip Richard Durbin, D-Ill., to tighten restrictions on employers who use H-1B and L-1 guestworker visas for highly skilled foreign workers. Durbin's amendment is opposed by the high-tech community but will likely attract support from organized labor and other Democrats who are uneasy with guestworker programs in general.
To keep the list of amendments at 12 for each party, Durbin's amendment will replace one by Sen. Barbara Boxer, D-Calif., that would have reduced the number of available guestworker visas annually by the number of visa holders who stay in the country beyond their two-year time limit.
Sen. Lindsey Graham, R-S.C., another of the bill's architects, said lawmakers are aware of concerns raised by Democrats that the bill's "point system" for granting green cards is unfair to families. But he tamped down reports that Senate Judiciary Immigration Subcommittee Chairman Edward Kennedy, D-Mass., is attempting to reach a separate deal on families.
"That's something we'll deal with in conference," Graham said.
Tuesday's vote gave the bill new life in the Senate, where it had languished after an earlier cloture vote failed. But conservative House Republicans stood their ground, holding a news conference on the Senate side of the Capitol to declare the bill would be dead on arrival in their chamber -- though they do not set the agenda.
Members of the Republican Study Committee also distanced themselves from President Bush, even as Bush was boosting the measure again at the White House.
"If you dislike the status quo on immigration, then you ought to be supporting a comprehensive approach to making sure the system works," Bush said just before the cloture vote was held. After the vote, White House spokesman Tony Snow said administration officials were "certainly pleased" by the outcome.
The RSC members, though, were certainly not pleased. "This bill increasingly is becoming a Democrat initiative ... and we want the folks of America to know what we're doing to try to stop it," said Rep. Pete Hoekstra, R-Mich. The House Republican Conference is expected to approve a Hoekstra motion expressing opposition to the Senate bill.
Christian Bourge and Keith Koffler contributed to this report.