Senators look like they’ll need a bit of Senate magic to bring the immigration bill to a swift conclusion, and even more of it to figure out a way to avert an increase in student loan interest rates.

Absent an agreement on amendments and yielding back debate time, senators face a long slog before inevitable passage of the immigration package with a significant majority backing it. Senators can shortcut anything by unanimous consent, but without that, here’s the timeline for the five remaining immigration votes:

• A vote to adopt the omnibus amendment that includes the “border surge” from GOP Sens. Bob Corker of Tennessee and John Hoeven of North Dakota could happen as early as 1 a.m. Wednesday.
• Right after that, the Senate would vote on a procedural motion to limit debate, or invoke cloture, on the amendment reported by the Judiciary Committee, with all the other changes added on the floor.
• The actual vote to adopt that substitute amendment would come due 30 hours thereafter, probably sometime before 8 a.m. Thursday.
• That would be followed by a vote on the cloture motion to bring to a close debate on the whole thing, with another 30 hours to wait before the vote on final passage.
• So, if Senate Majority Leader Harry Reid, D-Nev., finds that Republicans want him to grind through everything, the bill could still be done Friday afternoon, allowing him to meet his goal of getting out of town for the July Fourth recess with the immigration bill passed.

“You’re asking me a process question. I simply don’t know the answer,” McConnell said. “I do think we’re moving toward completion of the bill. It won’t surprise you to know that in a minority, we’d rather have more amendments rather than fewer. And we’re still hoping to get additional amendments. Whether we do or don’t, it looks to me like the bill is headed toward completion later this week.”

Under the current procedural situation, any additional amendment votes would require unanimous consent. Multiple senators said there’s work under way on an agreement that could include as many as 20 amendment votes, likely in exchange for cutting down on the amount of time that the Senate needs to burn before passing the bill.

Sen. Saxby Chambliss said that he wants to see changes to the bill’s agreement on agricultural employment. The Georgia Republican was one of several senators unable to make Monday’s test vote because of flight delays. He later announced he would have voted against limiting debate on moving ahead, which got 67 supporters.

“Right now, it’s frankly too easy under the base bill here in agriculture to get a green card, and it needs to be tightened up,” Chambliss said. “It’s too easy to get a green card … and that’s not what getting a green card should be all about, and it needs to be fair and equitable across the board.”

“We’re trying to get amendments down to a reasonable number,” immigration “gang of eight” member John McCain said. “A number of people want amendments. Now, whether it decides a vote or not is not totally clear.”

The Arizona Republican praised an amendment regarding E-Verify for employment that’s been championed by Sen. Rob Portman, R-Ohio. While it could have been included in the catch-all package that faced a successful test vote Monday, McCain said that Portman seeks a specific vote.

“I think it’s very good. I think both sides have agreed to it. He would like to have a debate, some more debate, discussion of it and a vote on it because he thinks it’s that important, and it’s not unusual for a senator to want that,” McCain said.

A Democratic aide signaled that an amendment agreement under discussion as the chamber broke for lunch Tuesday was facing objection from the Republican side.

Separately, a deal to avert an increase in student loan interest rates before July 1, looked like a long shot Tuesday afternoon, with Reid conceding that moving on the legislation quickly may not be possible.

Still, Reid said that he continued to meet with senators in both parties on the issue, including Republicans Lamar Alexander of Tennessee and Richard M. Burr of North Carolina, and Iowa Democrat Tom Harkin. Reid, McConnell, Speaker John A. Boehner, R-Ohio, and House Minority Leader Nancy Pelosi, D-Calif., were expected to talk about student loans, among other things, with President Barack Obama at the White House on Tuesday afternoon as well.

A lot of work ahead, it seems, but as Reid himself once said, “Always remember, because you’ve seen it as often as I have: Magic occurs on Thursday night.”