Colorado has become a focal point in the gun-control debate, as a package of restrictions on gun ownership advance through the legislature and appear on track to become law.

If that happens, Colorado will become the first state after New York to enact significant gun-control legislation in the wake of the December shooting in Newtown, Conn., and the first swing state to do so.

A state with a libertarian bent and a cultural history of gun ownership, for hunting as well as protection and recreation, Colorado has also been the site of two of the most high-profile mass shootings – this past August in the Aurora movie theater and Columbine High School in 1999. A swing state, it’s also under Democratic control for the first time in years (the governor, House, and Senate are all Democratic) – though many of those Democrats are moderates who are also champions of gun rights.

Last week saw heated debate in the state’s Capitol that went, in some cases, well into the night. Star national witnesses from both sides of the issue appeared to testify, including Mark Kelly, husband of former Arizona Congresswoman Gabrielle Giffords, shot by a Tucson gunman. At one point, a small plane flew overhead with a message for Gov. John Hickenlooper: “HICK: DO NOT TAKE OUR GUNS!”

Underscoring the importance of the Colorado outcome, Vice President Joe Biden has called some state lawmakers personally, while National Rifle Association head David Keene met privately with Governor Hickenlooper.

“There’s a lot at stake, and it’s been an incredible battle,” says Floyd Ciruli, a Colorado pollster and political analyst. “There’s a sense among the proponents [of the bills] that what comes out of Colorado may then have some influence on Washington thinking, and could definitely go into other states.”

What had grown into a package of seven bills has now shrunk to five. The bills still being considered include the following:

• A universal background check bill that would close some loopholes, including for private sales. The bill has passed both houses, and headed back to the House for another vote after passing the state Senate on Monday.

• A bill limiting magazine capacity to 15 rounds. Opponents had hoped they might have won over enough Democrats to kill it, but the bill passed the Senate Monday by one vote. Two Republican lawmakers said they will disobey it if it becomes law.

• A bill to keep guns out of the hands of those convicted of domestic violence offenses or under protection orders.

• A bill requiring in-person, rather than online, training for concealed carry permits.

• A bill requiring gun purchasers to pay for their own background check.

The background-check and magazine-limit bills have been among the most controversial – and, say proponents, could have the most effect.

“I think clearly Colorado is sending a message to the rest of the nation,” says Tom Mauser, a gun-control advocate since 1999, when his son, Daniel, was killed in the Columbine shooting. “It’s traditionally been a pro-gun state. I think the message is that you can be pro-gun and respect gun rights and still say that you’ve got to have some limits on things.”

Still, though the five bills have advanced through both houses (Democratic control of both houses is by a slim margin) and have the support of the governor, opposition has been fierce. Gun advocates have picketed the Capitol building, and lobby groups have threatened legislators from swing districts that they may suffer for their votes.

“What is pretty clear is that the approach by some of the Colorado legislators seems to be to try and put the burden of law on law-abiding people,” says NRA spokesman Andrew Arulanandam. “Whereas rational people realize that the focus ought to be on keeping guns out of the hands of criminals and those with mental problems who are predisposed to violence.”

Mr. Arulanandam also sought to minimize the national impact of the outcome in Colorado, either on other states or the federal government. “States are unique and sort of isolated in their actions,” he says.

Two highly controversial bills did not make it through last week, ultimately killed by their sponsors. One, backed by Senate president John Morse, would have made manufacturers and sellers of assault weapons liable for certain violent acts committed with those guns, if the gun buyer was someone who they “reasonably should have known might use the weapon” to cause harm. The other was a bill that would have banned concealed weapons on college campuses.

The liability bill, in particular, generated fierce criticism from many who labeled it as too extreme. “I think it generated an avalanche of e-mails,” says Mr. Ciruli, adding that “clearly, there are some boundaries out there.”

The bill banning concealed weapons on college campuses, meanwhile, became controversial after several Democratic legislators were portrayed as attacking or minimizing the experience of college rape survivors.

“I just want to say that actually, the statistics are not on your side,” State Sen. Evie Hudak told rape survivor Amanda Collins, after Ms. Collins testified about her experience being raped on a college campus. Though she had a concealed-carry permit, it was illegal on her Nevada campus to bring a gun on campus, and she wondered whether the outcome might have been different had she been armed.

Senator Hudak told her that statistics show that for every woman who uses a handgun to kill someone in self-defense, 83 are murdered by their attackers. But the remarks were portrayed as callous toward a victim, and followed remarks earlier in the week in which a House member suggested it was better for women to have call boxes, safe zones, and rape whistles than to be armed.

Colorado, which currently gets a “D” from the Law Center to Prevent Gun Violence, might move up to a C+ or B- if the current bills are passed, says Laura Cutilletta, a senior staff attorney at the center.

The background check, in particular, is important, and has been among the most popular measures for states enacting stricter gun laws, Ms. Cutilletta says.

“It’s a huge gap, a gaping loophole that we need to fill at the federal level … but that states have no choice but to do themselves. Colorado would be joining those states,” she says.

According to tracking by the Law Center, state legislatures have been active on both sides of the gun-control issue in 2013.

Over 600 bills strengthening gun-control laws have been introduced so far, an increase of 63 percent over the same time last year. Meanwhile, some 540 bills weakening gun-control laws have also been introduced – including bills in 34 states that would nullify federal firearms law in the state – a 14 percent increase.

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That Colorado is among the first to move to restrict gun rights is significant in part for the symbolism, says Cutilletta, particularly as the site of two high-profile shootings.

“I think it really sends a message to the federal government that this is a bellwether state, that this is where the thinking is going in a state like Colorado, and that says a lot,” she says. “It signifies that people are fed up and ready to do something about it.”