Two bills to expand gun rights that had been expected to fly through the Republican-controlled Texas Legislature have instead hit several snags and will need a big push during this final week of the session if they are to become law.

A so-called campus carry bill, which would allow concealed handguns in college classrooms, cleared the Senate in March and is scheduled for a House vote Tuesday. An open carry bill, which would permit guns to be carried in plain sight most everywhere, passed both chambers in different forms but ran into unexpected turbulence last week as a surprising coalition of Senate liberals and tea party conservatives teamed up for a vote to limit police oversight of the measure.

Both bills now are short on time if they are to be sent to Gov. Greg Abbott, who has pledged to expand gun rights in his first session as chief executive. The regular session ends June 1.

Campus carry has enjoyed majority support in the Legislature for years but has been stymied by fierce resistance from police and some higher education officials, notably within the University of Texas System.

New Chancellor William McRaven, the former head of U.S. Special Operations Command who spearheaded the covert raid that killed Osama Bin Laden, has told lawmakers that allowing concealed handguns in classrooms will make universities less safe and make it harder for schools to recruit and keep top faculty and staff.

Gun rights groups insist campus carry is an important self-defense measure for students and teachers and point to the mass shooting at Virginia Tech in 2007 in which the gunman killed 32 people.

The bill cleared the Republican-controlled Senate with ease, but a House vote has been delayed until this week amid squabbling between the chambers. Senate and House leaders finally agreed to put the issue to a vote this week as part of a broad deal on spending and tax cuts.

While campus carry efforts have percolated since 2009, the open carry debate has been a flashpoint of the 2015 session since January, when a Capitol confrontation between advocates and a Democratic lawmaker led to House members voting to make it easier to install panic buttons in their offices.

Law enforcement groups say open carry will increase pressure on police who may not know if someone is legally allowed to carry a weapon in public. Texas has about 850,000 concealed handgun license holders, and they would be allowed to openly carry their weapon in a shoulder or belt holster.

The Senate pushed the bill even further, and irked police, by putting in specific restrictions that would ban officers from asking someone carrying a gun if they were licensed if they had no other reason to stop them.

Libertarians said people carrying legal firearms shouldn't be stopped for obeying the law. Police call it a dangerous restriction on officers who wouldn't be able to determine if a convicted felon or someone with mental health problems was illegally armed.

Last week's Senate debate several times noted the recent biker shootout in Waco that left nine dead and wounded dozens more.

"The public don't realize how vulnerable they are until there is a shooting. Nobody is thinking about this like law enforcement officers do," said Charley Wilkison, executive director of the Combined Law Enforcement Associations of Texas, which opposes the restriction.

"Those who fear the question aren't constitutionalists -- they are criminals," Wilkison said.

Several Senate Democrats who oppose open carry joined the vote to support restricting police powers. They called it necessary to prevent racial profiling of minorities who may openly carry weapons.

"We know the people who would get stopped would more likely look like me, people of color," said Sen. Rodney Ellis a Houston Democrat who is black.