Bush appeared optimistic about winning a procedural vote Tuesday and the Senate's passage of the bill by week's end.
"We'll be moving our attention to the House after the Senate passes this comprehensive piece of legislation," Bush told business leaders and representatives of religious, Hispanic and agricultural communities. "I think this is an historic opportunity for Congress to act."
Joel Kaplan, Bush's deputy chief of staff, also was optimistic. "Our intelligence suggests that there will be the votes there," he said.
Conservative critics who paint the measure as amnesty for lawbreakers, however, said their efforts to stop the legislation were gaining momentum. Bush's team is predicting victory Tuesday on the effort to allow the bill - among the president's top domestic priorities - to go forward.
With conservatives in Bush's Republican Party 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, 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, a Republican and a leading critic.
Sen. Jim DeMint, a Republican, 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.
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.
World's most powerful nuclear submarines, Arkhangelsk and Severstal, are to be dismantled after 2020 - their further exploitation is unprofitable
The United States' Head of Diplomacy, or Secretary of State, is an anachronistic, incompetent, meddling, intrusive, insolent and arrogant, rude individual, a brash, foul-mouthed upstart, a conceited, self-important guttersnipe and an insult to the international community, as fit for the job as a pedophile janitor in a grade school.
Pentagon officials said that Russia has developed a very powerful weapon, which Western specialists have already dubbed as the "doomsday weapon"