In the eight days that elapsed between the Senate vote and the House vote, a gunman killed a woman at a synagogue in San Diego and another killed two people at the University of North Carolina at Charlotte. And as House lawmakers debated the legislation on Tuesday, news broke in Florida that a school resource officer’s holstered firearm went off at a Pasco County school cafeteria as the officer leaned against a wall. No one was hurt.

Several Republicans pointed to the San Diego shooting, in which a man said he rushed the shooting suspect, as a reason Florida should allow local school districts to partner with sheriff’s offices to train teachers who volunteer to do so to carry guns on campus.

“None of us want to be debating this,” Representative Byron Donalds of Naples, the only African-American in the House Republican caucus, said on Wednesday. “But the one thing that we have to acknowledge — as unfortunate as it is — is that when a psychotic person enters a facility, a school, where kids are at play or at study or at lunch and they pull a weapon, the first responders, the real first responders, are the school staff that love our children.”

Mr. Jones, 35, who suffered a serious nerve injury in 2016, was absent from Wednesday’s vote. His office said he had been rushed to the hospital on Wednesday morning suffering from vertigo, and was prescribed bed rest.

School districts in some of the state’s biggest cities, with large numbers of black and Hispanic students, have declined to participate in the guardian program, which was created last year after the shooting at Marjory Stoneman Douglas High School in Parkland that left 17 people dead and 17 wounded. The compromise worked out last year allowed certain school staff, but not classroom teachers, to be trained to carry guns.

In December, a state commission investigating the shooting recommended expanding the program to include classroom teachers. Investigators concluded that an armed teacher might have stopped the confessed attacker in Parkland. The provision was written into legislation that incorporated a slew of other commission recommendations relating to school safety and students’ mental health.