The lead Republican negotiator for what would be the US Senate's first gun control bill in a generation has walked out of talks with the Democrats, with doubts now being expressed over the legislation's future as the window before the mid-term elections in November narrows.
"This is the hardest part because at some point, you just got to make a decision,” Mr Cornyn said. “And when people don't want to make a decision, you can't accomplish the result. And that's kind of where we are right now.”
The Republican said "I'm not frustrated, I'm done", before later adding that he was open to continued discussions.
Hours after he walked out of talks, two people were killed and a third was injured when a gunman opened fire inside a church near Birmingham, Alabama.
Democratic and Republican senators were at odds over how to keep firearms from dangerous people as negotiators struggled to finalise details of a gun violence compromise in time for their self-imposed deadline to hold votes in Congress next week.
Lawmakers said they remained divided over how to define abusive dating partners who would be legally barred from purchasing firearms.
Disagreements were also unresolved over proposals to send money to states that have "red flag" laws that let authorities temporarily confiscate guns from people deemed dangerous by courts, and to other states for their own violence prevention programs.
The election-year talks had seemed headed toward agreement, with both parties fearing punishment by voters if Congress does not react to the carnage of last month's mass shootings.
A total of 31 people were killed at a grocery store in Buffalo, New York, and an elementary school in Uvalde, Texas. An outline of a deal has been endorsed by US president Joe Biden, senate majority leader Chuck Schumer, senate minority leader Mitch McConnell, and house speaker Nancy Pelosi.
Lawmakers have said a deal must be completed and written into legislative language by week's end if Congress is to vote by next week. It begins a July 4 recess after that.
Other negotiators seemed more optimistic, saying much of the overall package has been agreed to and aides were drafting bill language.
"A deal like this is difficult," Democratic senator Chris Murphy said when the meeting ended. "It comes with a lot of emotions, it comes with political risk to both sides. But we're close enough that we should be able to get there."
The measure would impose small curbs on firearms. It lacks proposals by Mr Biden and Democrats to prohibit assault-style weapons and high-capacity ammunition magazines like the ones used in Buffalo and Uvalde, or to raise the legal age for purchasing assault rifles from 18 to 21.
Even so, it would be Congress's most robust move against gun violence since 1993. A ban lawmakers enacted that year on assault weapons took effect in 1994 and expired after a decade.
Scores of high-profile mass shootings since have yielded little from Washington amid partisan deadlock, chiefly due to Republicans blocking virtually any new restrictions.