Legislation long pushed by the National Rifle Association that would allow people who are permitted to carry concealed guns in their home state to carry in every other state — regardless of local restrictions — stands a better chance than ever before of becoming federal law.

John Cornyn of Texas, the second-ranking Republican in the Senate, introduced a new version of a national “reciprocity” bill with 31 GOP co-sponsors on Monday. With a similar measure enjoying strong support in the House, and with President Donald Trump seemingly eager to support the NRA, the bill’s chances may rest on whether Senate Democrats can muster enough opposition to defeat it.

Cornyn told The Trace that he is “hopeful” the bill will receive support from enough Democrats to clear a 60-vote filibuster-proof threshold.

“All it is is a driver’s license for concealed carry,” Cornyn said. “If you can drive in Texas, you can drive in New York and follow New York laws.”

A Senate vote could be close. In 2013, in a vote that received limited attention amid a more prominent fight over tightening background check laws, 13 Democrats voted for a version of Cornyn’s bill. Seven of those senators — Jon Tester of Montana; Joe Manchin of West Virginia; Joe Donnelly of Indiana; Heidi Heitkamp of North Dakota; Martin Heinrich and Tom Udall of New Mexico; and Mark Warner of Virginia — remain in office.

Udall told The Trace that the 2013 vote reflects his general support for the concept of concealed carry reciprocity. The other Democratic senators who previously supported national reciprocity either did not respond to a request for comment or refused to comment, saying they had not reviewed the new legislation.

Senator Chris Murphy, a Connecticut Democrat who has led previous efforts in the Senate to tighten gun laws, is opposed to the bill.

“It’s playing down to the lowest common denominator,” he told The Trace.

The bill would allow any person “entitled and not prohibited from carrying a concealed firearm” in their home state to carry in other states, regardless of whether they meet permitting requirements in that state.

The differences between those requirements can be vast. Eleven states do not require any permit at all to carry a concealed gun in public, following New Hampshire’s enactment of a new law last week. Other states, like North Carolina and Ohio (among others), require would-be license holders to take firearms classes. And still others, like New York, impose so many restrictions that it can be nearly impossible to obtain a license.

On many other issues, from abortion to voting rights, Republicans have asserted the right of states to make their own laws, independent of the federal government. The Cornyn bill, if adopted, would be a significant departure from that ideology.

“The idea that Texas’s laws on guns should apply to Connecticut or New Hampshire or Vermont is absurd given Republicans’ traditional position on states’ rights,” Murphy said. “So we’ve got to call Republicans out for their hypocrisy.”

New York’s attorney general, Eric Schneiderman, a Democrat, previously told The Trace that a national reciprocity law would “undermine the core principles of federalism, the traditional police powers of state governments, and the safety of law enforcement officers across the country.”

The bill does make some allowances for local laws and ordinances. Out-of-state conceal-carry holders would still need to obey local restrictions on carrying guns in government buildings or schools, for example.

Many of the Democratic senators who previously supported national concealed-carry reciprocity are up for re-election in 2018. They will likely face lobbying from the NRA and other gun groups to support the bill. Their position this time may depend on how much pressure they receive from opponents of the measure, including groups like Americans for Responsible Solutions, headed by former U.S. Representative Gabby Giffords of Arizona and her husband, the astronaut Mark Kelly. The group held a news conference on Tuesday to express opposition.

Senate Minority Leader Chuck Schumer on Tuesday stopped short of saying he will urge fellow Democrats to oppose the bill, though he criticized the measure.

“I will certainly oppose it, and I would hope we would oppose it,” he said.

Senator Dianne Feinstein, a California Democrat, told The Trace that passing such a bill would be the “worst thing” she could imagine the Senate doing this year.

Murphy said he doesn’t think supporters of the legislation can muster 60 votes to overcome a filibuster.

In a bid to appeal to Democrats, Cornyn’s bill does not contain some of the more controversial provisions in a companion House proposal introduced by Representative Richard Hudson, a North Carolina Republican. Unlike the House bill, the Senate measure would not allow people to use an out-of-state permit to carry a gun in their own state, a loophole through which gun owners could duck more restrictive local laws. Cornyn’s bill also differs from Hudson’s bill by excluding provisions that would repeal a federal law creating gun-free school zones and allow people with out-of-state permits to personally sue police officers for damages that might result from being questioned about their weapons.

“They removed some of the harsher edges, but I wouldn’t overstate the importance” of those exclusions, said Lindsay Nichols, senior attorney at the Law Center to Prevent Gun Violence. “It’s pretty much doing the same thing.”

Cornyn said he does not expect his bill to receive consideration by the full Senate or by the Judiciary Committee before lawmakers tackle top Republican priorities, including repealing the Affordable Care Act and enacting tax cuts.