Senate Majority Whip John Cornyn (R-Tex.)  heads to the chamber for a procedural vote on a funding bill for the Department of Homeland Security  on March 2. (J. Scott Applewhite/AP)

This post has been updated.

Senators floated compromises Thursday aimed at breaking a deadlock that has gummed up the upper chamber's floor for nearly two weeks — holding up the confirmation of attorney general nominee Loretta Lynch — but key players stopped short of embracing any deal Thursday.

The Senate wrapped up its business for the week without taking action on the anti-human trafficking bill, and Majority Leader Mitch McConnell (R-Ky.) announced his intention to move on to the federal budget resolution on Monday, threatening to push the bill and the Lynch nomination well into April.

The Justice for Victims of Trafficking Act has been on the Senate floor since March 9, when Democrats — many of whom had voted to advance the bill through the Judiciary Committee — noticed and objected to an anti-abortion provision embedded in the bill. The language, a version of the "Hyde amendment" that has long been attached to appropriations bills, would prohibit a new trafficking victims compensation fund from being used for abortions.

Democrats cried foul, calling the provision an unprecedented expansion of federal restrictions on abortion and arguing that trafficking victims who have been forced into the sex trade, in particular, should not be subject to such restrictions.

Sen. John Cornyn (R-Tex.), the anti-trafficking bill's lead author and the majority whip, suggested on Thursday that the Hyde-like abortion provision could be left in the bill but the fund could be made "subject to appropriations" in a bid to overcome the Democratic objections. Democrats have said they believe the anti-trafficking bill would extend the abortion restriction to "non-taxpayer funds" -- in this case, fines from convicted traffickers -- for the first time.

"Now that we've made a proposal to them to give them what they've asked for and still preserve the 39-year limitation on the use of public dollars for abortion," he said, "can they take yes for an answer?" Cornyn asked on the Senate floor.

Not quite.

Sen. Patrick Leahy (D-Vt.), ranking member of the Judiciary Committee, said the Cornyn fix "does not solve the problem" since it would still, in the end, make the fines subject to Hyde language.

"This is not taxpayer money, and subjecting it to the Hyde Amendment would expand the amendment's reach to an offender-financed fund meant for women and children who should have all options available to them when it comes to health services after being sexually exploited," he said.

Leahy's suggestion: The Senate should take up a bill that passed the House last year which avoided the abortion debate entirely by authorizing the victims fund through standard taxpayer revenue rather than tapping offender fines.

Sen. Susan Collins (R-Maine) and Sen. Heidi Heitkamp (D-N.D.) came to the Senate floor late Thursday afternoon with a solution along those lines, one that would further "soften" the Cornyn offer, in Collins's words. Their amendment does not include any specific anti-abortion language, but it makes the victims fund subject to appropriations -- and application of the standard Hyde amendment.

"I don't know whether that will be acceptable to Sen. Cornyn, and I don't know if it will bring us enough Democratic votes to break this impasse, but it is a genuine effort by Sen. Heitkamp and me to try to move this bill forward," she said.

Cornyn did not appear inclined to completely remove the anti-abortion provision from the bill, even if it is all but certain to be applied during appropriations. And a leading Democratic senator also threw cold water on the Collins-Heitkamp compromise: "I am hopeful these conversations can continue and that we will reach an agreement as soon as possible," Sen. Patty Murray (D-Wash) said in a statement. "But as I have made clear, I will not support an alternative that expands harmful restrictions on women’s reproductive rights, including this latest proposal."

If a solution is not hashed out by Monday, it is almost certain that the anti-trafficking bill would be tabled for at least three weeks, with the Lynch nomination also languishing. The Senate is now set to take up the federal budget Monday, a process expected to consume most of the week, with a two-week recess to follow.

A third consecutive day of votes to break the Democratic filibuster failed on Thursday, with Republicans still two short of the 60 votes necessary to close debate and move forward.

Before the Senate adjourned, Cornyn said that if no compromise were reached Thursday, discussions would continue through the weekend.