The U.S. Senate voted 68-31 on Thursday to cut off a filibuster by a group of far-right Republicans and allow debate on a new gun safety measure aimed at preventing the kind of tragedies that occurred at Sandy Hook Elementary in Newtown, Connecticut. According to USA Today, 16 Republican Senators voted with Democrats to stop the filibuster, which was led by Tea Party favorites like Sens. Rand Paul (R-KY), Mike Lee (R-UT) and Ted Cruz (R-TX).

Two Democrats voted against ending the filibuster, Sen. Mary Landrieu (LA) and Mark Begich (AK), both of whom are Democrats from heavily Republican states who are up for re-election this cycle.

Majority Leader Sen. Harry Reid said that now the amendment process will begin, including measures proposed by Sens. Joe Manchin (D-WA) and Pat Toomey (R-PA) to expand background checks on guns purchased at gun shows and online.

While the Senate bill does not include a ban on the sale of assault-style weapons, it does increase penalties on "straw purchasers," people who buy guns for individuals who are banned from owning them. It also includes limits for gun magazine sizes, allocates grant funds for school security and expands background check procedures.

Republicans who voted to end the filibuster included Sens. John McCain (AZ), Kelly Ayotte (NH) and Johnny Isaacson (GA).

UPDATE: In a statement released Thursday afternoon, Laura W. Murphy, director of the ACLU’s Washington Legislative Office, said, "As the Senate moves forward on gun control legislation, it’s important that we don’t punish the kids we are trying to protect. The ACLU will be paying close attention to potential civil liberties issues as amendments are filed in the coming days. While well-meaning policymakers might assume that adding more police or school resource officers makes students safer, experience demonstrates otherwise. Our focus should be on our children, not law enforcement."

Murphy also said that steps must be taken to ensure a measure of privacy with regard to background checks. "Those checks have to be conducted in a way that protects sensitive health records and does not discourage people from seeking drug treatment, and we hope our concerns are addressed as the bill is amended," she said.