Cornyn said his amendment would have allowed citizens issued conceal and carry licenses in their home states to have their firearm legally in other states. He said it would “treat conceal and carry licenses like a drivers license.”

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Sen. Bob MenendezRobert MenendezThe Mideast-focused Senate letter we need to see Taiwan deserves to participate in United Nations The way forward on the Iran nuclear deal under President Trump MORE (D-N.J.) criticized Cornyn’s amendment, saying it would turn a “positive” conversation about protecting the nation’s children into a “feather” in the cap of the National Rifle Association (NRA).

“The amendment is basically mandatory conceal and carry reciprocity,” Menendez said. “This amendment forces states to accept other states’ conceal and carry permits. … So much for states’ rights.”

The Senate is considering the Safe Communities, Safe Schools Act, S.649, which would expand background checks on gun purchases, crack down on gun trafficking and beef up security in schools. 

GOP senators have vowed to block that bill, claiming it goes too far and infringes on the rights of gun-owners.

“We should not be making it harder for law abiding citizens to execute their rights,” Cornyn said ahead of his vote Wednesday.

Cornyn said that those supporting stricter background checks for gun purchases should also support his amendment because “a conceal and carry license is like a background check on steroids.” But Menendez countered that the amendment could potentially increase gun violence, rather than decrease it.

The Senate was scheduled to vote on nine amendments Wednesday, all of which were subject to a 60-vote threshold. More amendment agreements are possible later this week.