Editor's note: This story has been updated throughout.

A bill lifting some of the state's restrictions on handguns cleared the Texas Senate along a party line vote of 20 to 11 Monday.

Senate Bill 17, from state Sen. Craig Estes, R-Wichita Falls, would allow concealed weapons permit holders to carry holstered handguns openly. It is the first measure to come to the Senate floor not related to Gov. Greg Abbott's emergency items

“In other states that have taken this step … it’s been deemed pretty much a non-event,” Estes told his colleagues as he introduced the legislation. “We have searched really hard far and wide for problems, and we haven’t found any.”

After the upper chamber takes a final vote on the measure, it will head to the House.

State law currently allows the open carrying of long guns like rifles and shotguns. Handguns may only be carried in a concealed fashion by those who obtain a license.

During a four-hour debate, lawmakers in the upper chamber considered almost two-dozen amendments to the bill. Most were offered by Democrats — who made various attempts to soften the bill including calling for increasing training, background checks, and other licensing requirements to obtain a handgun — and almost all failed along straight party lines.

State Sen. John Whitmire, D-Houston, came close to shouting as he argued in favor of an amendment exempting the Capitol complex from open carry if it passes.

Relating his experiences dealing with angry or mentally ill individuals before his committee, Whitmire said it would now be easy for such a person to grab handgun out of a holster to use it to attack bystanders.

“It’s dead wrong…to say there’s not disturbed people in this building,” said Whitmire, who chairs the Criminal Justice committee. “It’s not if it’s going to happen it’s when it’s going to happen, and you know it and I know it.”

Estes called such a circumstance “far-fetched.”

Democrats also argued that the change would increase risk to police officers responding to the scene of the crime, who might now be faced with several people with firearms and have no way to determine the bad actors.

“Have you thought about what dangers you’re fixing to expose on law enforcement?” asked Whitmire during the debate, noting the widespread opposition to such a law from the state’s police associations.

SB 17 is among a slate of high-profile gun bills up for consideration this session. So far it is one of two that have made it out of committee. The other is Senate Bill 11, which would allow handgun license holders to carry their firearms on college campuses. Both bills passed along party lines 7 to 2, only opposed by the panel's Democrats.

Though all 20 Senate Republicans supported Estes’ proposal, at least one did so with reservations.

State Sen. Don Huffines, R-Dallas, rose before the chamber took a vote to say Estes' bill did not go far enough in restoring Second Amendment rights.

“I will vote for SB 17 but I do so with a very heavy heart,” said Huffines, who described the merits of so-called “constitutional carry” legislation.

Favored by vocal factions within the gun rights movement, constitutional carry bills would repeal handgun permitting rules altogether. It has yet to receive committee hearings in either chamber.

A House panel is set to consider two gun bills — one permitting open carry with a license and another allowing concealed carry on college campuses — Tuesday morning.