Opponents say it would make campuses more dangerous -- adding the potential for typical college disputes over grades, romances and fraternity rivalries to become deadly -- and also could lead to more suicides.
Wentworth said similar dire warnings were made in 1995 when Texas passed its concealed weapons law.
"Opponents predicted it would be the wild, wild west; there would be blood on the streets," Wentworth said. "None of that has happened."
The bill still faces significant hurdles to become law before the June 1 end of the legislative session.
It still needs a final Senate vote -- which could come as early as Wednesday -- before it goes to the House. A similar House bill died when it ran up against a legislative deadline.
If passed, Wentworth said Texas would join three other states -- Utah, Colorado and West Virginia -- in allowing license holders to carry the concealed weapons on campus. Texas is one of several states to consider similar legislation this year.
The Texas bill allows private schools to ban weapons from campus. But the Senate rejected several attempts to make the ban optional for public schools and to create gun-free dorm rooms.
A ban on taking weapons to college sports events would not change.
Wentworth said allowing guns on campus will protect student safety. At Virginia Tech, 32 people were gunned down before the shooter killed himself. Last year, a gunman at Northern Illinois killed five and wounded 18.
"I would feel personally guilty if I were to wake up some morning and find out on some Texas college campus, a similar tragedy had happened," Wentworth said of the Virginia Tech massacre. "They were picked off like sitting ducks in the classroom."
Opponents argue allowing guns won't prevent similar scenarios and will confuse law enforcement if they arrive on a crime scene and find several people carrying weapons.
"We don't need to incentivize campus Rambos," said Sen. Rodney Ellis, a Houston Democrat who voted against the bill.
"It makes us feel like we've gotten tough -- deputizing students -- but the fact is that the universities don't want it and law enforcement doesn't want it because they know it will not make our campuses safer," Ellis said.
The bill is supported by the National Rifle Association and Students for Concealed Carry on Campus, a group that claims more than 37,000 members across the country.
It also has run into fierce resistance from other campus groups. At the University of Texas, which has its own history of shooting violence, the idea has met stiff opposition.
Charles Whitman's 1966 shooting rampage from the top of the university tower killed 16 people and wounded dozens more. It stood as the worst campus shooting in history until the Virginia Tech bloodbath.
The UT student government, the graduate student assembly and the faculty advisory council have all passed resolutions against the campus guns bills.
Texas graduate student John Woods was a Virginia Tech student in 2007 and his girlfriend was among those killed. He has helped organized resistance to the Texas bill.
"The Senate voted against allowing a student to be in a gun-free dorm room; this shows exactly how little concern our lawmakers actually have for student safety," Woods said.
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