More than half the members of the House have co-signed the legislation. The state Senate passed a similar bill in 2009, and Gov. Rick Perry has said he supports the idea, The Associated Press reports.
Those in favor of allowing concealed weapons at colleges say it would allow students and professors to protect themselves in the event of a campus shooting, like the Virginia Tech massacre in 2007. In September, a University of Texas student went on a shooting rampage on campus before killing himself in the school's library. No one else was hurt.
"The only option now is to hide behind their desks or play dead," David Burnett, spokesman for Students for Concealed Carry on Campus, said last week, according to the Austin American-Statesman.
If passed, the legislation would make Texas the second state to allow concealed weapons on college campuses, after Utah. Colorado allows colleges to decide for themselves.
Similar legislation has been proposed in several states, including Arizona, Nevada, Oklahoma and Wisconsin. In January, a state senator from Nebraska proposed a law to allow school administrators and security personnel to carry guns in primary schools. And one school district in Texas, Harrold Independent, began allowing guns in its single school in 2007.
Last week, victims of Virginia Tech shooter Seung Hui Cho lobbied in Austin against the measure. Colin Goddard, who was shot four times but survived by playing dead, told the Statesman that adding guns to the equation will not make anyone safer.
"I was there that day. It was the craziest day of my life, with one person walking around with two guns," Goddard said. "I can't even imagine what it would have been like with multiple students and multiple guns."