Congressional Democrats on Tuesday introduced a bill that would move toward universal background checks for firearms.

In introducing the bill, Speaker Nancy Pelosi (D., Calif.) described gun violence as “an epidemic in our country that must be stopped.”

The legislation, which would require criminal background checks on any gun sale, is expected to pass the House but would face steep hurdles in the Republican-controlled Senate. While checks are currently required for most gun sales, some private, online, or gun-show sales can legally be completed without checks of a buyer’s record.

There would be limited exceptions, including for law enforcement officers and for guns transferred between close family members.

The bill is the first piece of national gun-control legislation with a hope of passing in even one chamber of Congress since attempts failed after the 2012 Sandy Hook Elementary School shooting in Newtown, CN. The move to introduce the bill was timed to mark the eighth anniversary of the mass shooting in Arizona that nearly killed former Representative Gabrielle Giffords.

Jennifer Baker, director of the lobbying arm of the National Rifle Association, said in a statement, “Instead of looking for effective solutions that will deal with the root cause of violent crime and save lives, anti-gun politicians would rather score political points and push ineffective legislation that doesn’t stop criminals.”