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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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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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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"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."

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."

A state prosecutor in Tijuana, Mexico is warning that three recent murders in the town along the United States border display similar characteristics to the killings of notorious serial killer Ted Bundy.

"This subject has criminal tendencies associated with violent and psychopathic behavior," Baja California Attorney General Ricardo Iván Carpio told reporters in Tijuana, KSWB-TV reported. "His profile is very similar to someone who became very well known decades ago: Ted Bundy."

Carpio said that three of the 1,859 homicides recorded in Tijuana, which sits directly across the U.S. border and 20 miles south of downtown San Diego, exhibit signs of a killer who seduces vulnerable women, convinces them to meet in private setting, and then subjects them to violent sexual acts before murdering them.

In addition to the similarities in the way the crimes are carried out, Mexican authorities believe the suspect is an American who traveled across the border and have notified American authorities of the killer’s possible identity in hopes of apprehending him in the United States.

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"We are in communication and are coordinating with other institutions to locate and capture this individual," Carpio said.’

The suspected killer found his victims at strip clubs and bars in the Zona Norte community of north Tijuana and each woman was found dead in a hotel room, KNSD-TV reported.

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The Federal Bureau of Investigation did not immediately respond to a request for comment from Fox News Digital.

Ted Bundy, one of the most prolific serial killers in American criminal history, confessed to 30 kidnappings and murders of women and girls across seven states between 1974 and 1978. 

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Bundy was known for his personable nature and was able to lure women in public places into situations where he could abduct them by force before beating, strangling, raping, and ultimately killing them. 

Bundy was executed by electric chair in 1989 after being sentenced to death in Florida. 

"Without a doubt, we’re going to detain him, and we’re going to extradite him to Baja California where he will be processed," Carpio told reporters about the hunt for the killer.