Senators are going to take another whack at immigration reform this week and while it appears the bill has a better chance of survival the second time around, no one could say for certain Friday whether it would make it to a vote on final passage.

Both Republicans and Democrats cautioned that the deal to bring the bill back up is just that, and not an agreement to actually pass it at the end of the week. So while the legislation likely will clear its first 60-vote hurdle on Tuesday, when the Senate effectively votes on whether to proceed to the bill, Senators will have to take as many as 24 potentially bill-altering votes before deciding whether to support the final product.

Indeed, Majority Whip Dick Durbin (D-Ill.) said Democrats’ ability to prevent a filibuster, or invoke cloture, likely would be “dependent on 20 different amendments.”

One Senate GOP leadership aide agreed that the amendment process could be rocky.

“This is by no means a slam-dunk,” the aide said, adding that the first cloture vote on Tuesday “is going to be an exciting vote.”

Still, Senate Majority Leader Harry Reid (D-Nev.) struck an optimistic tone Friday, saying, “We feel confident we can get a bill. … I think we’re going to find next week that this debate should go well.”

Even so, Durbin has warned Republicans repeatedly that Democrats will be able to muster no more than 37 votes of the 60 needed to invoke cloture on the motion to proceed to the bill.

“Thirty-seven votes is our high-water mark,” said Durbin on Friday. “We may not be able to get that again.”

But even if Democrats can deliver those votes, Republicans will still have to produce at least 23 votes — a feat GOP backers of the bill said is doable but not assured.

Sen. Jon Kyl (R-Ariz.), a key supporter of the bill, told reporters on Friday that negotiators had agreed to try to consider as many amendments as possible before forcing a final cloture vote on the bill.

“Most Members would like to have an idea of what has passed or failed,” before deciding whether to support an end to debate.

While most of the dozen or so Members who crafted the immigration bill have agreed to oppose amendments that would substantially alter their original deal, some also are attempting to make changes that may or may not sit well with wavering Members of both parties.

Kyl, for example, is pushing an amendment with Sen. Lindsey Graham (R-S.C.) that would require law enforcement agencies to crack down on foreign visitors who overstay their visas, permanently bar visa overstayers from coming back, and prohibit sex offenders and gang members from entering the country.

The proposal also would require background checks to be completed before any temporary worker applicants are given probationary “Z” visas. Currently, the measure would require those visas to be handed out within 24 hours, regardless of whether the background check has been completed.

Though Kyl said the bipartisan group supporting the bill does not oppose his amendment, it is unclear whether its likely adoption could turn off some fence-sitting Democrats.

Meanwhile, Kyl indicated that Republican backers of the measure might take flight if a plan by Sen. Bob Menendez (D-N.J.) is approved.

Menendez’s amendment would give greater weight to people with family already in the United States when they apply for temporary status under the new merit-based system to be created by the bill. That system, as it is now written, stresses employment history and education over familial relations.

While declining to call it a “deal killer,” Kyl said the proposal would “upset the rather delicately balanced merit-based system.”

But Menendez defended his amendment.

“When the family reunification amendments come up, all we hear is ‘killer amendment,’ ‘heart of the deal’ and other doomsday dialogue,” Menendez said in a statement. “But I don’t for one second buy that rhetoric. We’ve seen other so-called killer amendments pass, and the [bipartisan negotiators] didn’t walk away from the deal.”

Kyl also said he expected to defeat various proposals, such as one by Sens. Barack Obama (D-Ill.) and Chuck Grassley (R-Iowa), that would eliminate or rework portions of the bill requiring employers to verify the citizenship of their workers, in part, through tamper-resistant IDs.

The bill was on the Senate floor for two weeks earlier this month, but a majority of Republicans and a dozen Democrats successfully filibustered it. However, several Republican bill sponsors, who nevertheless supported the initial filibuster, say they will vote to move forward now that Reid and McConnell have agreed to the list of 24 amendments.