After coming under withering criticism from government transparency advocates over their refusal to take up a bill requiring Senators to file campaign finance forms electronically, Senate Republicans on Tuesday attempted to call the measure up for consideration — but with a catch.

The bill, which would change current law that only requires Senators to file paper campaign finance forms, has been blocked for months by an anonymous Republican “hold” that has prevented the majority Democrats from bringing up and passing the bill without amendment.

But as Majority Leader Harry Reid (D-Nev.) was attempting Tuesday to appoint conferees for a larger lobbying and ethics overhaul package, Republican Sen. Bob Bennett (Utah) attempted to obtain consent to bring up the electronic filing bill along with a mystery amendment to be offered by Minority Leader Mitch McConnell (R-Ky.) or “his designee.”

McConnell spokesman Don Stewart said Republicans do not object to the substance of the electronic filing bill, but to the process under which Democrats have attempted to bring it up.

“What’s stopped the bill in the past is they want to do it without debate and without amendment,” Stewart said.

He added that Bennett only asked for two hours of total debate time on the bill. “It’s not an unreasonable amount of time, and it’s not unreasonable to have one amendment,” Stewart said.

Reid objected to Bennett’s request, as Bennett subsequently did to the appointment of conferees on the lobbying and ethics bill. But Reid held out the possibility that a deal could be reached.

“Once we look at the amendment, we may be willing to accept it,” said Reid, adding that the Bennett request was an obvious “effort to divert attention from ethics and lobbying reform.”

Stewart said Republicans did not have a specific amendment in mind when making the request.

Sunlight Foundation Executive Director Ellen Miller, whose organization has spearheaded the publicity surrounding the GOP hold on the measure, said she did not believe that Bennett’s motives in bringing up the bill were pure.

“I think Senator Bennett is playing games,” she said on Tuesday. The bill, she added, “ought to go through without any parliamentary tricks and that includes poison pill amendments. And that appears to be what he was trying to do this afternoon.”

A Bennett spokeswoman said he made the request on behalf of McConnell.

Still, Miller said her “best guesstimate” was that the amendment would be a Bennett proposal — strongly favored by McConnell — to allow political parties to coordinate their expenditures with their candidates, a practice current law prohibits.

Bennett originally planned to offer the amendment during consideration of the bill in the Senate Rules and Administration Committee in March, but dropped the proposal after securing a promise from Rules Chairwoman Dianne Feinstein (D-Calif.) to hold a hearing on the matter in April, which she did.

After objecting twice to Democratic requests to take up and pass the electronic filing bill, Republicans have come under scathing criticism over the past few months, in part because of Sunlight’s unsuccessful campaign to root out the GOP Senator or Senators who placed the anonymous hold on the bill by having constituents call Senators’ offices to ask.

Sunlight also recently bought ad space on a billboard in Louisville, Ky., asking “What’s McConnell Hiding?” and telling people to call his office to register their complaints. They also have a contest in which $500 will go to the first person who captures McConnell on video either revealing the anonymous Senator or explaining why he won’t.

“I suspect they are feeling some pressure to move this legislation,” Miller said.