Thune made the comments minutes after Senate Minority Leader Chuck Schumer (D-NY) sent Republicans a proposal that contained nine reforms to how DHS should conduct immigration enforcement after the death of two protesters in Minneapolis.

House Minority Leader Hakeem Jeffries (D-NY), leaving a meeting with Schumer at the Capitol, said Democrats still consider tighter warrant requirements and a ban on officers wearing face masks as “absolutely essential” to striking a deal.

Schumer called the offer a “good-faith proposal that contains some of the very same asks Democrats have been talking about now for months.”

In a floor speech, Schumer argued that Democrats stand ready to negotiate “at a moment’s notice,” though Thune said not to expect a new proposal from Republicans.

“There’s no point in doing that,” he said. “Honestly, this is retreading ground that we’ve been treading for weeks, and, frankly, starting to go on months.”

Instead, Thune announced that he would hold another vote on DHS funding later on Wednesday that excludes around $5 billion earmarked for Immigration and Customs Enforcement removal operations. The exclusion represents a concession on the part of Republicans, who sent their own offer to Democrats over the weekend.

The legislation includes money for body cameras and de-escalation training that Republicans brokered with Democrats in January, before the death of a second protester.

“Later today, we’re going to trigger a vote,” Thune said. “They said over the weekend that they didn’t want to fund ERO, they’ll fund everything else — so, we’re going to give them an opportunity to vote to do that.”

Jeffries told the Washington Examiner that the offer from Republicans was not “close” to what Democrats need for a deal. His meeting with Schumer is part of a flurry of activity at the Capitol as lawmakers frantically search for an end to the impasse, which is approaching the 43-day shutdown record set last year.

Sen. Katie Britt (R-AL), the lead negotiator on DHS funding for Republicans, also met with three centrist House Democrats at the Capitol on Wednesday to discuss a possible compromise.

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When asked if lawmakers should stay in town until an agreement is reached, Jeffries said, “We need to resolve this issue. We should resolve it this week.”

Thune has previously suggested Republicans could cancel some or all of the April recess if a deal does not come together.