President Bush's team is predicting victory Tuesday on the effort to allow the bill among the president's top domestic priorities to go forward.

"We're optimistic," said Joel Kaplan, Bush's deputy chief of staff. "Our intelligence suggests that there will be the votes there."

Conservative critics who paint the measure as amnesty for lawbreakers, however, said their efforts to stop the legislation were gaining momentum.

With GOP conservatives determined to block the legislation, backers need 60 votes to clear procedural hurdles and resurrect it Tuesday. Just 45 senators only seven of them Republicans supported such a move two weeks ago.

Bush has mounted an unusually personal effort to diffuse bitter 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.

Still, after a chaotic several weeks in which the measure survived several near-death experiences, it remains buffeted by intraparty divisions. Bush's aides say they are lobbying hard to persuade Republicans that the measure deserves support.

"We're in the phase now, as (senators) head into the final tally of the votes, of making the case and explaining why we think the status quo is unacceptable," Kaplan said.

Jim Manley, spokesman for Senate Majority Leader Harry Reid, D-Nevada, said the Senate's top Democrat is hopeful that there will be enough converts to push the bill forward.