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A Republican senator who was one of the lead negotiators on a firearms and mental health bill that passed this year indicated there's no time left in December to pass more significant legislation on guns, a sign that this top Democratic priority may fall by the wayside.

"I don’t think that’s on the table," Sen. John Cornyn, R-Texas, told Fox News Digital on Wednesday when asked about the chances of movement on what Democrats call an assault weapons ban. Cornyn, who helped negotiate the Bipartisan Safer Communities Act that Congress passed this summer, would likely be a key GOP vote for any future gun legislation.

Additionally, a Democrat senator who has been vocal on gun control, Richard Blumenthal of Connecticut, told Fox News Digital that the Senate "has a lot on our plate" when asked about the prospect of passing a last-minute gun bill.

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John Cornyn speaks to reporters gun control

"I don’t think that’s on the table," Sen. John Cornyn, R-Texas, said about a last-minute assault weapons ban. (Brandon Bell/Getty Images)

Blumenthal said that as of today, there are "probably not 60 votes" for a bill, a sign that there are not 10 Republican senators willing to break a filibuster and allow a bill to pass. But Blumenthal said he would still prefer a vote on some bill, even if it fails.

"I personally would like to be on the record," he said.

Comments from Cornyn and Blumenthal are just the latest sign that Senate Majority Leader Chuck Schumer's goal of passing an assault weapons ban before the end of the current Congress is slipping away.

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Richard Blumenthal gun control

Sen. Richard Blumenthal says he "personally feels the need to vote. … I personally would like to be on the record" on the assault weapons ban. (Chip Somodevilla/Getty Images)

On Wednesday, Blumenthal joined his Democrat colleague, Dick Durbin, D-Ill., and the March Fourth Coalition, an anti-gun advocacy group, to host a press conference aimed at urging the Senate to pass the assault weapons ban in the lame-duck session.

Schumer is facing pressure from the White House, too.

President Joe Biden was scheduled to speak at the 10th annual National Vigil for All Victims of Gun Violence on Wednesday evening, just a week before the 10-year mark of the Sandy Hook Elementary School shooting massacre in Newtown, Connecticut. Following the shooting at Club-Q in Colorado Springs, Colorado, Biden said he would renew calls for the Senate to pass the ban.

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Senate Majority Leader Chuck Schumer gun control

FILE - Schumer said last week, "The bottom line is that I am the author of the assault weapons ban. I believe in it strongly." (AP Photo/J. Scott Applewhite)

"The idea we still allow semi-automatic weapons to be purchased is sick. Just sick," Biden said during a press event in Nantucket on Thanksgiving Day. "I’m going to try to get rid of assault weapons."

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Schumer said last week, "The bottom line is that I am the author of the assault weapons ban. I believe in it strongly. And we're continuing to work to see the best way we can try to get this done."