The Senate working group negotiating a bipartisan deal on the border is closing in on a compromise that will allow leadership to move tens of billions in aid for Ukraine.

Senate Majority Leader Chuck Schumer (D-NY) wants to put the White House’s request for aid on the floor as soon as this week, but that timeline is largely dependent on how quickly the border security agreement, demanded by Republicans in exchange for further Ukraine funding, materializes.

The negotiators have been stuck on the issue of parole, even as they’ve found common ground on changes to asylum policy. However, Sen. Chris Murphy (D-CT) said on Monday that talks were finally “wrapping up” following the weeks-long impasse.

“Our work is largely done,” he told reporters after a meeting with Schumer.

Murphy, the lead Democratic negotiator, declined to say if all of the remaining sticking points had been resolved, but he did note that legislative text was being finalized. The current step, he said, is for appropriators to assess the monetary impact of the tentative agreement.

Schumer tamped down expectations on Monday that a deal was imminent. “We remain hopeful, but it’s certainly not a done deal yet,” he said from the Senate floor. “There are a handful of issues that have not yet been agreed to.”

And even Murphy expressed concern that appropriators could upend negotiations by “relitigating” the terms of the deal. But the shift in focus represents the latest sign a deal is at hand after two months of talks.

“It’s always tough at the end, but we’re doing great,” Sen. Kyrsten Sinema (I-AZ) said after meeting with Republican leadership on Monday.

If a deal is announced, it’s unlikely Ukraine aid can pass this week. Leadership will need to whip votes once the text is released, and the Senate conservatives opposed to further funding have already indicated they will slow down the legislative process.

But Schumer could take the first procedural step toward moving the legislation, with the hope of sending a bill to the House after it returns from a weeklong recess.

Party leadership has attempted to inject a sense of urgency into passing the supplemental, which also includes assistance for Israel and Taiwan. President Joe Biden convened a meeting at the White House last week to underscore the “critical importance” of the aid.

Republican leadership in the Senate will make much the same case on Wednesday in a conference meeting on Ukraine requested by conservatives.

But the big question is whether the Republican-led House takes up the legislation. Senate conservatives can only delay the bill, not sink it.

Speaker Mike Johnson (R-LA) has threatened to reject any legislation that does not include “substantive” border policy changes but has simultaneously expressed a desire to continue arming Ukraine. Hanging over that decision is Donald Trump, who is urging Johnson to torpedo the emerging compromise.

Senate Republicans have already begun to counter the influence of the former president, arguing Republicans won’t get another shot at border reforms if they don’t act now. Sen. John Thune (R-SD), the No. 2 Republican in the Senate, insisted on Monday that provisions in the deal would help Trump clamp down on the flow of immigrants if he wins a second term. 

“These are really important fixes to border policy that would be great tools available not only now but to a future administration,” he told reporters.

Regarding a vote count in the Senate, Thune said that winning over a majority of his conference would be “helpful” to getting the bill through the House. “That’s certainly the goal,” he said.

Sinema, an independent closely involved in the talks, noted that process starts with the Republicans most inclined to support a deal.

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“This is a middle-out strategy, right? This is a package that will start in the middle, folks like me, then you move out to the edges and get as many votes as you can on both sides,” she said.

“But yeah, not everyone’s gonna be happy,” she added.