The bipartisan legislation would also allow accusers to file complaints without being forced to sign a nondisclosure agreement.
The briefing came as Alabama voters went to the polls in a hotly contested Senate race.
The briefing followed President Donald Trump's controversial decision to recognize Jerusalem as the capital of Israel.
Sen. Al Franken will resign after new allegations and growing calls for his resignation.
Sexual misconduct accusations will force 2018 congressional election candidates to weigh whether their past behavior could doom their chances.
Podesta added that "it is extraordinary that we would see something like this just 11 days out from a presidential election."
A representative for the Clinton campaign said the team had "no idea" what the FBI director was referencing in his Friday letter.
Hillary Clinton said that her campaign found out about FBI Director James Comey's letter after it was sent to lawmakers.