Loretta Lynch’s bid to be the next attorney general remains mired in Senate politics, but Republicans offered a proposal Tuesday that could lift a major hurdle to a floor vote on her nomination.

Democratic leadership, however, remains opposed to the deal from Majority Whip John Cornyn, R-Texas, and it’s not clear if enough members of the rank and file would sign on to the Cornyn offer. The proposal would alter abortion-related language Democrats have objected to in a human trafficking bill, a legislative fight that has no connection to Lynch or her qualifications.

Still, Republicans have declined to hold a confirmation vote for Lynch until after the chamber dispenses with the trafficking bill. Democrats so far have blocked that bill because of a provision that would prevent the fines and penalties collected from human traffickers—a victim’s fund—from being used to fund abortions.

Caught in the debate is Lynch’s nomination, now pending before the full Senate for almost 50 days. That’s nearly twice as long a wait as the past seven attorneys general combined, Sen. Patrick J. Leahy, D-Vt., said on the Senate floor Monday.

To add to the legislative muck, Cornyn said his proposal uses the abortion-related language in yet another bill about to hit the Senate floor, the House-passed package (HR 2) to repeal Medicare’s oft-criticized sustainable growth rate formula for paying physicians, or SGR. House Minority Leader Nancy Pelosi, D-Calif., negotiated the abortion-related language in that bill, Cornyn pointed out to reporters.

Sen. Patty Murray, D-Wash., said the provision in the SGR bill language does match the so-called Hyde amendment, which for years has prohibited federal funds for being spent on abortions. But that is very different than the trafficking bill on the Senate agenda, which for the first time applies Hyde language to non-taxpayer dollars.

“That is a bridge we are not going to allow to be crossed,” Murray said at a press conference outside the Senate chamber. Democrats have offered Cornyn nine proposals at this point and he has rejected every single one of them, Murray added.

“We are trying to work our way through this,” Murray said. “But I will tell you at the end of the day we will not accept language that simply hides the Hyde. If the Hyde language is in it and is extended for the first time ever to non-taxpayer dollars, that is a non-starter for us.”

Cornyn called Murray’s concerns a “red herring,” because fines and penalties become the U.S. government’s money and subject to the appropriations process.

The new language in the trafficking bill would make it clear that any money going into the victim’s fund would have to be appropriated, and therefore subject to Hyde, Cornyn told reporters.

The Republican solution might be aiming to win over the Democratic leadership, but just a small number of Democratic defectors.

Four Democrats have voted for cloture on the human trafficking bill already, Cornyn said, so Republicans “only need two more in order to get to a solution.”

“I’m hopeful that we’ll get those votes and we’re certainly talking to everyone who will listen,” Cornyn said.

A cloture vote could be held as early as Wednesday on the human trafficking bill, Cornyn said.

Minority Leader Sen. Harry Reid, D-Nev., told reporters Lynch would be confirmed. “She is going to be attorney general of the United States,” Reid said at a press conference Tuesday.