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Senate Republicans say they are seeing progress in talks on potential border policy changes to be included in a supplemental spending package requested by the White House, although it isn’t clear if a deal is possible.

Talks have been ongoing between Senate lawmakers and the administration over a supplemental funding request that includes border funding as well as aid for Israel and Ukraine.

But Republicans and Democrats have found sharp disagreement on the contents of the border funding section, with Republicans demanding stricter limits on initial asylum screenings and the use of parole. House Republican leadership has called for the inclusion of a broader package passed in the chamber earlier this year, but Senate Republicans have shown openness to a more limited package.

MIGRANT ENCOUNTERS AGAIN TOP 10K IN SINGLE DAY AS LAWMAKERS EYE NEW BORDER LIMITS

Biden walking with border officials

President Biden walks along the border wall in El Paso, Texas, on Jan. 8. (Jim Watson/AFP via Getty Images)

President Biden said last week that he was open to "significant compromises," and CBS News reported Tuesday that the Biden administration is open to a new Title 42-style authority, which was the COVID-era order that allowed for the rapid expulsion of migrants at the southern border until May this year.

The administration was reportedly also open to a nationwide expansion of expedited removal, which allows for recently entered migrants to be quickly removed if they do not meet the initial asylum standard. It is currently only being used at and near the border. CBS reported that the White House was willing to mandate the detention of certain migrants as their claims are considered.

While that report has sparked anger from left-wing Democrats, Republicans have responded positively, if cautiously.

"It's a start, but I think the most important thing is the White House has finally gotten engaged, and it's taken a long time to get there, but they finally did on Monday," Sen. John Cornyn, R-Texas, told reporters. "But unfortunately, we're so late in the year and with so little time left, it's not practical to conclude between now and the end of the year."

Sen. Thom Tillis, R-N.C., said he is open to the idea of having something like the Title 42 authority, citing the large number of migrant encounters at the southern border, and said that lawmakers should stay in Washington until a deal can be hammered out. Lawmakers are scheduled to leave D.C. for their winter break on Thursday.

Migrants are processed in Eagle Pass, Texas, on Tuesday.

Migrants are processed in Eagle Pass, Texas, on Tuesday. (Fox News)

"I'm going to take it as a good-faith offer, which is why I think we have to act in good faith and stay here until we get it negotiated out," he said.

5,000 ILLEGAL IMMIGRANTS RELEASED EVERY DAY INTO US, ADMIN OFFICIALS PRIVATELY TELL LAWMAKERS

Multiple lawmakers told reporters that there was nothing yet in writing from the White House and that the key would be in the details.

"We've been back and forth this morning, and we'll continue to be able to work through. And again, yesterday was positive and we made a lot of progress on it to be able to go through it, and we'll just keep working," said Sen. James Lankford, R-Okla.

Sen. Lindsey Graham, R-S.C., said that it was "good news" that the White House was involved in talks.

"Whether we can land this plane, I don’t know," he said.

However, even if a package can be agreed to in the upper chamber, it is unclear if the agreement would gain the assent of the House, which has been eyeing more expansive moves. Meanwhile, Democrats in both the House and the Senate took aim at the reported proposals, blasting the Biden administration for what they see as a return to Trump-era policies.

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"It is truly shameful that President Biden and his administration are considering selling out migrants and asylum seekers in order placate extreme Republicans who are jeopardizing our national security and that of our allies just to score a political point," Sen. Bob Menendez, D-N.J., said in a statement.

Meanwhile, Fox News reported that Tuesday saw another day in which overwhelmed officials at the border encountered more than 10,000 migrants in a single day.

Fox News' Tyler Olson and The Associated Press contributed to this report.