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(CNN) —  

The Senate leaders of both political parties released a rare joint statement Wednesday, saying they expect to quickly pass long-stalled sexual harassment legislation that would overhaul the system through which Capitol Hill handles such cases.

“We want to commend Senators Blunt and Klobuchar, who have worked tirelessly and in a bipartisan way, to address this serious issue,” said Senate Majority Leader Mitch McConnell and his Democratic counterpart, Sen. Chuck Schumer of New York. “With this agreement, both parties are coming together to update the laws governing how the Congress addresses workplace claims and protecting staff and others from harassment. We’re optimistic that after our members review the legislation, this bill will pass the Senate in short order.”

The legislation was formally released Wednesday from Missouri Republican Sen. Roy Blunt and Minnesota Democratic Sen. Amy Klobuchar. The two senators, the chief negotiators of the deal in the Senate, presented the outlines of the plan Tuesday during their respective party’s policy luncheons and it was received positively by Democrats and Republicans.

’Nothing about it felt right’: More than 50 people describe sexual harassment on Capitol Hill

With McConnell and Schumer’s stamp of approval, the bill will now be quickly moved in the Senate – likely bypassing committee process and being brought directly to the floor of the Senate for a vote. McConnell could announce those steps soon.

Senate aides tell CNN that the hope is to get it passed this week in the Senate. But if that slides it would have to wait two weeks until after the Memorial Day recess.

The House of Representatives passed its version of the bill in February, which would reform the Congressional Accountability Act, which set up the process for handling sexual harassment complaints on Capitol Hill and hold lawmakers personally liable for paying settlements, rather than allowing them to use taxpayers’ money out of a little-known account of the US Treasury.

Should the Senate pass the bill, it would need to either be sent back to the House again or go to conference committee taken up by a conference committee.

The biggest difference between the House and Senate bills centers around the language of members liability for sexual harassment and discrimination claims. The Senate’s version aims to tighten up the language to make very clear when members would be required to pay for settlements – and when they would not.

Senate lawyers felt the way the House bill was written left the lawmakers potentially open for a member to legally be responsible to pay the settlement if a staff member’s wrongdoing led to a settlement. The Senate bill would outline more clearly if the member was responsible for the misdeed, they would pay out of their own pocket. If a member of the staff is responsible, the settlement would still come out of the US Treasury fund, using taxpayer money.

The member would be on the hook for all settlements from their own misconduct, including other forms of discrimination such as gender, race and age discrimination. The member’s liability would be capped at $300,000 – as the legislation writes they would be on the hook for “compensatory damages” which are already limited in current law at $300,000.

Among a few other changes, the Senate bill would also require reporting of settlements and awards paid only once a year, whereas the House bill calls for reporting semi-annually.

Senators from both parties had long pushed for a bill to address sexual harassment. One of the most vocal critics of the delay, Democratic Sen. Kirsten Gillibrand of New York, said Tuesday’s announcement was an “important step forward.”

“By passing this reform, we can finally make sure that when a member of Congress sexually harasses or discriminates against someone on their staff, the taxpayers are not left holding the bag, and it finally removes the barriers that were preventing many victims of harassment and discrimination from reporting what had happened to them, like the absurd ‘cooling off period’ before a formal complaint could even be filed,” Gillibrand said.