WASHINGTON — President Joe Biden and top congressional leaders met at the White House on Wednesday as the Senate inched closer to a bipartisan immigration deal that would unlock critical military aid for Ukraine.

Optimism about an agreement reached an all-time high before the meeting as Senate Majority Leader Chuck Schumer, D-N.Y., and Minority Leader Mitch McConnell, R-Ky., told reporters they expect it to come together soon.

“We are closer than we have ever been,” Schumer said. “For the first time, I think the chances of getting it done in the Senate are greater than not getting it done.”

The top Democratic negotiator in the talks concurred.

“I’ve been a part of enough negotiations to know when you’re coming close to finishing, and I feel like we’re there,” Sen. Chris Murphy, D-Conn., told reporters. “But didn’t I say something like that last three weeks ago?”

Leaving the White House, House Speaker Mike Johnson, R-La., called Wednesday’s meeting “productive,” saying he told Biden and Democrats: “We must have change at the border — substantive policy change.”

Johnson and House conservatives had been pressing the Democratic-led Senate to take up their Republicans-only border bill, known as H.R. 2. But after Wednesday’s meeting, Johnson seemed to soften that demand, saying: “We’re not insistent upon a particular name of a piece of legislation, but we are insistent that the elements have to be meaningful.”

He also described Ukraine aid as a “necessity” but added that “we must insist that the border be the top priority.”

Schumer called it a “very good meeting,” saying there was “a large amount of agreement around the table” about the need to address immigration, as well as aid for Ukraine.

“There are a couple of people in the room who said let’s do border first. We said we have to do both together,” Schumer said, adding that national security adviser Jake Sullivan told lawmakers in the meeting exactly when Ukraine would run out of munitions without additional U.S. assistance.

“It was very powerful,” Schumer said.

House Foreign Affairs Committee Chair Michael McCaul, R-Texas, described what Biden told participants: “He said that I’m ready to make significant changes to the border. He said it was broken. He knows that it needs to be fixed.”

McConnell said earlier Wednesday he expects that the Senate could vote on the emerging immigration package — tied to Ukraine aid, Israel funding and assistance for Taiwan — next week.

“We have a number of important international responsibilities. And I think it’s time to go ahead with the supplemental, and I’m anticipating it’ll be before us next week,” he said.

That prompted a speedy rebuke from Rep. Chip Roy, R-Texas:

And Wednesday, a group of 17 conservative Senate Republicans sent a letter to GOP Conference Chairman John Barrasso of Wyoming, requesting a special conference meeting to discuss concerns about Ukraine funding. Barrasso quickly scheduled the meeting for next Wednesday.

But even if an immigration and foreign aid package can clear the Senate, it’s unclear what happens next. House members have not been involved in the talks between senators and administration officials.

Johnson had said the emerging Senate immigration deal would be a nonstarter in the House. On Wednesday, he declared: “I don’t think now is the time for comprehensive immigration reform, because we know how complicated that is. You can’t do that quickly.”

One possibility is that the House and the Senate could go to conference and have negotiators from each chamber try to hammer out a deal.

Wednesday’s gathering in the Cabinet Room was the first formal meeting between Biden and Johnson (though the two briefly spoke in October when Johnson and other Hill leaders received a classified White House briefing on the supplemental). The meeting also comes at a pivotal moment in Washington as political leaders juggle other important matters; Congress needs to pass a short-term stopgap measure by Friday night to avert a government shutdown and buy itself more time to pass its 12 appropriations bills.

In addition to Johnson, Schumer and McConnell, others at the meeting included House Minority Leader Hakeem Jeffries, D-N.Y., and the Democratic and Republican leaders of the House and Senate committees that oversee appropriations, foreign affairs, military and intelligence matters.

White House chief of staff Jeff Zients, National Intelligence Director Avril Haines and budget director Shalanda Young were among the administration officials in attendance, according to the White House.

“Our goal is to give the executive branch more tools to better manage the border while living up to our values as a nation of immigrants,” Murphy said Wednesday. “This is the most complicated area of American statute. And so it’s not surprising that it’s taking us some time to work out the final few issues and get those resolved into text.”

This article was originally published on NBCNews.com