"I am pleased to introduce legislation that strikes a balance between states' rights and individuals' Second Amendment rights outlined by the Constitution," Thune said. "Rather than establish a national standard, our bill will ensure that law-abiding citizens are able to carry concealed firearms while at the same time respecting the laws of the respective states they visit."

Thune has introduced similar legislation before, and in 2009 it received 58 votes in support — a majority, but two shy of the 60 votes needed to dodge a filibuster under Senate rules.

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Thune's bill is similar but not identical to legislation that passed the House in November with the support of 40 Democrats, H.R. 822. But Thune's bill is different in that it would allow people from states that allow concealed carry without a permit to also carry without a permit in other states, something the House-passed bill does not allow.

Two Senate Democrats, Mark BegichMark Peter BegichPerez creates advisory team for DNC transition The future of the Arctic 2016’s battle for the Senate: A shifting map MORE (D-Alaska) and Joel Manchin (D-W.Va.), have proposed a Senate companion bill to H.R. 822 that they believe can be passed, in particular because it is more respectful of the rights of states that do have permitting requirements.

A spokeswoman for Begich noted that the National Rifle Association (NRA) supports the Begich bill.

Co-sponsors on Thune's bill include Judiciary Committee ranking member Chuck GrassleyCharles (Chuck) Ernest GrassleyGrassley blasts Democrats over unwillingness to probe Clinton GOP and Dems bitterly divided by immigration Thanks to the farm lobby, the US is stuck with a broken ethanol policy MORE (R-Iowa), former committee ranking member Orrin HatchOrrin Grant HatchMcConnell names Senate GOP tax conferees Ryan pledges 'entitlement reform' in 2018 Utah governor calls Bannon a 'bigot' after attacks on Romney MORE (R-Utah) and others, including Sens. Rand PaulRandal (Rand) Howard PaulLexington mayor launches bid for Congress Trump-free Kennedy Center Honors avoids politics Meet the Iran hawk who could be Trump's next secretary of State MORE (R-Ky.) and Marco RubioMarco Antonio RubioRyan pledges 'entitlement reform' in 2018 Richard Gere welcomes lawmakers' words of support for Tibet Dem lawmaker gives McConnell's tax reform op-ed a failing grade MORE (R-Fla.).

— This story was updated on March 21 to reflect the differences in Thune's bill and the one proposed by Sens. Begich and Manchin.