(NewsNation) — Senators will meet Tuesday to discuss what the framework of a bipartisan gun reform package would look like, just one week after a gunman opened fire at a Texas elementary school, killing 19 children and two teachers.

The Democrats first attempted to respond to the mass shooting with a domestic terrorism bill in the Senate last week that would have opened debate on difficult questions surrounding hate crimes and gun safety. The bill was blocked.

The domestic terrorism bill that failed last week dates back to 2017, when Rep. Brad Schneider, D-Ill., first proposed it after mass shootings in Las Vegas and Southerland Springs, Texas.

Democratic Sen. Chris Murphy and Republican Sen. John Cornyn are two of the lawmakers set to virtually meet, with a 10-day deadline to strike a deal according to the Associated Press.

Encouraging state “red flag” laws to keep guns away from those with mental health issues and addressing school security and mental health resources were on the table, said Murphy, who is leading the effort.

Senate Republican leader Mitch McConnell, who has said little about gun legislation since the several tragedies have unfolded, told reporters he met with Cornyn earlier and encouraged senators to collaborate across the aisle on workable outcomes.

“I am hopeful that we could come up with a bipartisan solution that’s directly related to the facts of this awful massacre,” McConnell said.

The Texas tragedy, which came less than two weeks after another mass shooting at a grocery store in Buffalo, New York, has refocused Biden’s presidency on one of the greatest political challenges of his career — the long fight for gun control.

A day after visiting Uvalde and pledging, “We will,” in response to people chanting, “Do something,” President Joe Biden on Monday expressed some optimism that there may be some bipartisan support to tighten restrictions on the kind of high-powered weapons used by the gunman.

“I think things have gotten so bad that everybody’s getting more rational, at least that’s my hope,” Biden told reporters before honoring the nation’s fallen in Memorial Day remarks at Arlington National Cemetery.

“The Second Amendment was never absolute,” Biden said. “You couldn’t buy a cannon when the Second Amendment was passed. You couldn’t go out and buy a lot of weapons.”

The Associated Press contributed to this report.