According to POPVOX, the Senate has now introduced its version of the National Reciprocity bill; the House version was passed on NOV 16.
https://www.popvox.com/bills/us/112/s2188
There are also some other interesting bills listed:
The Straw Purchaser Penalty Enhancement Act (HR 4190)
Enhances criminal penalties for straw purchasers of firearms.
Weigh in at
https://www.popvox.com/bills/us/112/hr4190
HR 3814
Prohibits the Justice Dept. from tracking and cataloguing the purchases of multiple rifles and shotguns.
Weigh in at
https://www.popvox.com/bills/us/112/hr3814
The Gun Trafficking Prevention Act (S 1973)
Makes it illegal to traffic or assist in the trafficking of a firearm, including straw-purchasers who buy a gun for someone else (according to the bill sponsor).
Weigh in at
https://www.popvox.com/bills/us/112/s1973
The Second Amendment Enforcement Act (HR 645)
Restores Second Amendment rights in the District of Columbia.
Weigh in at
https://www.popvox.com/bills/us/112/hr645
The Second Amendment Protection Act (HR 3594)
Expresses the sense of the Congress that the U.S. should not adopt any treaty that poses a threat to the right to keep and bear arms -- and to withhold funding from the United Nations if it restricts or infringes upon the rights of U.S. individuals to keep and bear arms.
Weigh in at
https://www.popvox.com/bills/us/112/hr3594