AUSTIN, Texas - A few Texas lawmakers want to strengthen state gun laws that they say could have helped prevent Sunday's mass shooting.

The Democratic House members say there's no reason to allow people to openly carry long rifles, and current law prohibits police from questioning people unless they're committing a crime.

"They could not have stopped (the shooter) and asked him, 'Hey, do you have a concealed handgun permit? Are you even someone who can legally buy a weapon?' That would've been illegal," said Rep. Poncho Nevárez, D-Eagle Pass, a gun owner himself. "The first time they would have been able to ask him anything or do anything is when he leveled the weapon off and started firing it."

The lawmakers also want to make state background checks for licenses to carry made public and shared with the FBI.

"Nobody is trying to take away any law abiding person's guns," said Rep. Gina Hinojosa, D-Austin. "This is about keeping guns out of the hands of criminals."

Sunday's shooter should not have been able to purchase a firearm based on his history of domestic violence, but federal officials were kept in the dark.

"We have had three mass shooters who passed the NICS (National Instant Criminal Background Check System) background check and shouldn't have," said former Republican Texas Land Commissioner Jerry Patterson.

While he was a state senator in 1995, Patterson authored the state's concealed handgun law. He encourages current lawmakers to be deliberate about passing new laws.

"People are screaming, 'We have to do something. We have to do something.' Wrong," he said. "We have to find something that would have a positive impact and do that."

He supports sharing license information with the FBI, but Patterson stopped short of saying it should be made public. Patterson said he would also support extending the review period for gun purchases beyond the current three-day limit. However, that is a federal matter.

The Democratic lawmakers said Wednesday they applaud efforts by Sen. John Cornyn and others to audit NICS oversights and require people convicted of domestic violence to surrender guns the owned previous to the conviction. Existing law only bans them from buying more guns.