On the other side, Sen. Jeff Sessions, R-Ala., said opponents of amnesty for illegal immigrants are being told they must vote for the bill anyway "because that's the only way we're going to create a legal system of immigration in America."

Under the bill, he said, "we're not going to get any substantial reduction in illegality, we're going to double illegality."

President Bush and his team were working intensely to rally support for the measure.

"It's a careful compromise," the president told business leaders and representatives of religious, Hispanic and agricultural communities. He said, "In a good piece of legislation like this, and a difficult piece of legislation like this, one side doesn't get everything they want."

Bush was working the phones to drum up backers, said Commerce Secretary Carlos Gutierrez, who with Homeland Security Secretary Michael Chertoff was also lobbying senators.

Tuesday's vote suggested that key senators and White House officials had succeeded — at least for now — in bargaining with skeptical lawmakers for a second chance to pass the bill. Several senators who have been promised votes on their amendments, including Sens. Kit Bond, R-Mo., Barbara Boxer, D-Calif., Norm Coleman, R-Minn., Pete Domenici, R-N.M., John Ensign, R-Nev., and Jim Webb, D-Va., supported moving ahead with the measure, after siding with opponents earlier this month on the test vote that stalled it.

Less clear was whether that support would hold. At least one Democrat who backed reviving the bill, Sen. Robert Menendez of New Jersey, publicly said he could not guarantee he would vote later to end debate and move to final passage.

Menendez is pushing for passage of his amendment to award more points in a new merit-based green card allocation system for family ties to U.S. citizens or legal permanent residents.

Several of the Republican amendments slated for Senate 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.

Likely to be among the first voted on is a proposal by Sen. Kay Bailey Hutchison, R-Texas, to require all adult illegal immigrants to return home before gaining permanent lawful status. The bill would require only heads of households seeking green cards to do so.

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.