Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) warned on Thursday that the Senate will vote on a disaster aid package before they leave for a weeklong break, even as negotiators struggle to reach a bipartisan agreement.

“The Senate will not adjourn this week until we have voted on legislation to deliver long-overdue relief funding for communities that have been hit hard by natural disasters," McConnell said from the Senate floor.

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He added that negotiators have to reach an agreement on Thursday if it's going to pass before lawmakers leave for the Memorial Day recess, but "one way or another, the Senate is not leaving without taking action."

McConnell hasn't said what the Senate will vote on without an agreement, but Republicans are expected to bring back up a proposal the chamber rejected in April.

"I think if we don't know something in the next couple of hours, then we'll probably end up having to vote on something that we voted on before, but hopefully they'll get a deal," said Sen. John Thune John Randolph ThuneOvernight Defense: Stopgap spending measure awaits Senate vote | Trump nominates former Nunes aide for intelligence community watchdog | Trump extends ban on racial discrimination training to contractors, military Remote work poses state tax challenges Senate GOP sees early Supreme Court vote as political booster shot MORE (S.D.), the No. 2 Senate Republican.

Thune added that Senate Republicans were set to hold a caucus meeting later Thursday, where they would likely get a sense of whether or not there was going to be a deal.

Talks are stalled over how much of the administration's $4.5 billion request for emergency border money to include in a package. The thorny issue includes political landmines like Immigration and Customs Enforcement (ICE) and detention bed funding.

Top members of the Senate and House Appropriations committees had been expected to meet on Wednesday evening to try to iron out the remaining roadblocks, but that meeting was canceled amid a standoff over the immigration and border issues.

Aides said on Thursday morning that negotiations were ongoing, but immigration-related provisions were still a sticking point even as lawmakers only have hours to craft an agreement.

Asked if the top appropriators were planning to get in a room to try to hash out a deal, similar to how the government shutdown ended earlier this year, a Democratic aide said there were no plans and that it's "so technical I don’t think it would be useful."

"Obviously, time is running short," the aide added when asked about the chances of reaching a deal on Thursday.

The White House's $4.5 billion border request included $3.3 billion for humanitarian assistance. About $1.1 billion would go toward operations such as expanding the number of detention beds and providing more investigation resources.

Democrats have agreed to include humanitarian aid as part of an agreement on the disaster package, but a previous offer didn't include the administration's request for more money for ICE detention beds, considered a non-starter for most of the caucus.

Democrats made another offer to Republicans late Wednesday night as staff-level talks continue to try to find a way of breaking the stalemate. But Republicans have also warned that attempts by Democrats to use the bill to pass new immigration-related restrictions would be counterproductive to getting a deal.

"I think they're trying to get the language in a place where both sides can be satisfied," Thune said. "But you know the prescriptive language that the Democrats in the House are trying to add to this, I think they're trying to work through how to … massage the language in a way that both sides can walk away and feel like they got what they wanted."

Senate Minority Leader Charles Schumer Chuck SchumerCruz blocks amended resolution honoring Ginsburg over language about her dying wish Senate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' MORE (D-N.Y.) argued on Thursday that if negotiators can't reach a deal within a matter of hours, they should drop the border-related language from the bill and only pass a "clean" disaster aid bill.

"If we can't come to an agreement this morning on other extraneous issues that the House is discussing, we should set those issues to the side," Schumer said. "We should pass the disaster agreement as is."

Immigration's emergence as a sticking point comes after lawmakers managed to work out several other issues. They say they've reached a deal on aid to Puerto Rico, despite Trump's previous criticism of the island territory, and Republicans have jettisoned harbor maintenance funding and a short-term extension of the Violence Against Women Act.

— This report was updated at 11 a.m.