When the Senate passed its immigration overhaul Thursday, one amendment lauded by Democrats and Republicans wasn’t in it.

That’s because — as both sides agree — Sen. Rob Portman, R-Ohio, declined to have his proposal to expand the E-Verify system included in the major bipartisan catchall amendment that the Senate crafted last week.

But that’s where the agreement ends and the fight between Portman and Senate Majority Leader Harry Reid, D-Nev., begins.

Portman desperately wanted a separate vote on an amendment he developed with Sen. Jon Tester, D-Mont., that would enhance workplace verification of citizenship. But he said the deal to include it, along with a bipartisan border security amendment, in the June 21 substitute amendment came with too many strings attached.

Portman said that including the language in the Corker-Hoeven “border surge” package would have required him to co-sponsor the amendment “sight unseen.” But Reid’s office categorically denies the suggestion that any such communication came from the Democratic side.

“Senator Portman was offered the opportunity to co-sponsor Hoeven-Portman if he so chose. If he declined to co-sponsor, his E-VERIFY changes would still have been included in the bill,” a senior Democratic aide said in an email Wednesday night. “There was no ‘price of admission’ whatsoever.”

Portman responded to Reid’s office Thursday, saying that he offered another idea that’s somewhat deep in the weeds of Senate procedure.

“Do they also dispute that we gave them a pathway forward as a second-degree amendment and gave them the language … [the] parliamentarian having approved it, that they could have offered Portman-Tester as a second amendment without going through UC?” asked Portman. “We would have filled the tree.”

“Filling the tree” is one of the most-frequently deployed devices in the majority leader’s toolbox. In effect, Reid uses his traditional power of first recognition to insert a bunch of dummy amendments and motions that block the offering of further amendments. When he does this, he has the option of putting substantive text in the placeholders, but doing so may infuriate other senators when their amendments remain blocked.

Reid’s office says that granting such treatment to Portman’s plan would have been unrealistic. That’s a point that seems to bear out, considering that earlier in the debate on the immigration measure, Sen. Mary L. Landrieu, D-La., blasted the idea that consensus amendments had to wait in line behind more contentious offerings from senators who had no plan to support the final bill.

Portman stressed that his bipartisan amendment was not like that, and said that without it, he would vote against final passage.

“I think it is in a unique class in that we have all the sign-offs from ‘gang of eight’, White House, AFL-CIO, Chamber of Commerce, I mean we did our work over the last six weeks, and it strengthens the bill,” he said.

New York Democratic Sen. Charles E. Schumer, a member of the gang of eight that negotiated the underlying measure on Wednesday countered Portman’s argument that his language was imperative.

“I have heard my good friend from Ohio, and I like his amendment. In fact, my staff worked on it with him. But let’s make no mistake about it. This is a vast bill, and E-Verify — permanent E-Verify — is in the bill. Maybe it can be improved a little bit, but it is 0.01 percent of the bill,” Schumer said. “It does not deal with border security. It does not deal with entry-exit. It does not deal with the 11 million. It does not deal with future flow.

“Of course, we want this amendment offered, and many of us will support it. But to say that is the only reason — if it does not get in the bill it is not worth voting for — I would have to respectfully and completely disagree with my colleague,” he added.

On Thursday, Portman reiterated his belief that simply packaging his language into an omnibus amendment wouldn’t give it significant clout in potential House-Senate negotiations.

“In the conference committee, you want to be able to say, you know what, we really need to get tough on the workplace, as hard as it is politically,” Portman said, explaining that there could be more leverage in conference if there’s an overwhelming standalone vote. “I think we could get not just 76 votes on E-Verify, I think we could get closer to 80 or 90.

“I don’t think it would, it would send the message that needs to be sent,” as part of the omnibus amendment, said Portman.