This comes nearly two years after the Virgina Tech massacre where 32 students were gunned down.
"I think if even one person would have had a gun in the last incident, a lot fewer people would have lost their lives," said University of Texas at Arlington employee Amy Lindley.
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Texas is one of seven states currently considering this type of legislation.
Of the 150 House members, 70 support the bill. Twelve of 31 senators have also signed in support.
"Ultimately, I think it's a good idea," UTA faculty member Phyllis Adams said, "I think sometimes you just need to be prepared, but I think everybody needs to be very responsible and accountable."
While some support the legislation, opponents said it would bring fear into the classroom.
"If the person sitting next to me taking a test has a gun, I would be like, 'Oh man!'" said UTA student Dzong Huih.
Others said it would put professors, staff and students at added risk.
"For any minor incident they may think it's bad enough that they might pull a gun." said staff member Terrie Davis.
In order to get a concealed handgun license in Texas, applicants must be 21 years old, go through special training, and pass a criminal background check.