Senators urging the passage of a bill that would legalize millions of illegal immigrants hope to revive bipartisan support for the embattled measure and push it to passage by week's end.

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-Nev., said the Senate's top Democrat is hopeful that there will be enough converts to push the bill forward.

Those against the plan to provide a path to citizenship to illegal immigrants were undeterred. "The enthusiasm for this bill, even the votes for this bill, have been eroding," said Sen. Jeff Sessions, R-Ala., a leading critic.

Sen. Jim DeMint, R-S.C., said proponents are engaging in "arm-twisting" to corral support, and he appealed to a skeptical public to ratchet up pressure on their senators to kill it.

"We do still have a shot to stop it, but it's only going to be if the American people raise the level of their voices in the next 24 hours," DeMint said.

The legislation faces still more trials even if it scales its initial obstacle, with votes looming on amendments that could alter key parts of the measure. Another make-or-break test vote could come as early as Thursday.

Reid is planning to use a rare maneuver known as a "clay pigeon" to advance a set package of Republican and Democratic amendments and lay the groundwork for quick votes on them.

DeMint, Sessions and other conservative foes of the bill wrote Reid on Monday complaining that the procedure would "shut off the debate" and "silence amendments," thus trampling senators' rights.

In a pointed response, Reid conceded the procedure was unusual, but he called it necessary to block a Republican filibuster. The move has the support, Reid wrote, of their own GOP leader, Sen. Mitch McConnell of Kentucky, and the White House.

Several of the Republican amendments slated for 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.

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.

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.