A leading opponent of immigration overhaul legislation argued that a procedural vote Tuesday was tantamount to voting on passage, while others said the bill’s fate would hang on how it is shaped by amendments.

A GOP leadership aide and the White House predicted Monday that enough Republicans are prepared to join Democrats to limit debate on the motion to proceed to the bill (S 1639).

That would keep the measure alive and allow the Senate to begin debate on nearly two dozen amendments, using a rare procedure called a “clay pigeon” to speed the normally slow Senate process.

After most of the amendments have been acted on, another cloture vote would come on the bill itself, probably Thursday.

Bill opponents say they fear that by that time, Senate leaders and the White House will have created enough momentum to carry the legislation to passage.

Bush has been calling senators to drum up support, and the White House indicated that would continue this week as needed.

In this case, “momentum” might be another word for “mathematics.” If bill supporters can get 60 votes on Tuesday, the amending process would have to yield a major substantive change to the bill — making it either more or less palatable to one side or the other — to alter the outcome substantially over the next few days.

Republican Lisa Murkowski of Alaska said she intends to support Tuesday’s vote to proceed, but has yet to make up her mind beyond that.

“There’s 24 amendments that have yet to be resolved,” Murkowski said. “It’s voting to get to the bill, and that’s what I think we need to do.”

A leading bill opponent painted that as almost quaintly naive.

Republican Jim DeMint of South Carolina said any senators who support the motion to proceed are casting a vote for the bill, even if they intend to vote against the measure on final passage.

DeMint argues that once the process starts, the momentum of the debate will carry the chamber toward final passage — and 51 votes will be there in the end. He said he counts 34 senators who will vote “no” on the procedural motion, and there are “10 to 12 votes still in play.”

Those 10 to 12 senators are subject to “a lot of arm-twisting” by the White House and Senate leaders, DeMint said.

The only way to stop them and block supporters from getting the 60 votes needed to limit debate is if “the American people raise the level of their voices in the next 24 hours,” he said.

“I think we still have enough votes in play to stop it,” DeMint said. “I think it is a long shot when you are working against so many powerful forces. But the most powerful force in this debate has been the American people, and they are continuing to let their voices be heard.”

Others were working with roughly the same vote counts.

“We’re optimistic that the 60 votes will be there tomorrow,” Joel Kaplan, President Bush’s deputy chief of staff, told reporters on a conference call. “We’ll see soon enough, but our intelligence suggests that there will be the votes there to move on to the bill and to begin considering amendments.”

Majority Whip Richard J. Durbin, D-Ill., estimated needing between 22 and 25 GOP votes to reach the 60-vote threshold needed to invoke cloture on the bill.

Durbin said the best pro-cloture count for Democrats is 37, the same number that supported a third and final cloture vote on an earlier version of the bill (S 1348) on June 7. They were joined that day by seven Republicans and Joseph I. Lieberman, I-Conn.

Durbin is among those, like Murkowski, who believe that the outcome later in the week will be shaped by what happens to the amendments that are considered after Tuesday’s vote — if it succeeds.

“Depending on 20 different amendments, [it] could create a different outcome on cloture,” said Durbin.

One of DeMint’s allies in the opposition, Jeff Sessions, R-Ala., agreed with that assessment. He said Tuesday’s vote was “critical” but “not necessarily fatal” to opponents’ hopes of killing the bill.

The amendments address a range of touchy issues, from Democratic concerns about family reunification to Republican demands for stronger enforcement. Any one of them could rattle the process again.

Friend and foe alike agree that regardless of the outcome Tuesday, if the amending process changes the bill in a substantial enough way to make the second cloture vote fail, then immigration would be dead for the 110th Congress.

“If there are amendments [adopted] that are offensive to Democratic senators, we won’t produce 37 votes,” Durbin said. “And if there are amendments that are offensive the other way, you can imagine the result.”