Must first face Democratic opponents in Aug. 8 primary
President Joe Biden opposes measure.
Karine Jean-Pierre made comments during Thursday's briefing
Adam Michael Nettina voicemail referred to Nashville school massacre
Queer Youth Assemble organized events across the country
U.S. Rep. Robert Garcia (D-Calif.) among measure's sponsors
Measure passed by 213-208 vote margin
Advocacy groups condemned the law
Republican Gov. Ron DeSantis signed bill on March 16
Measure would extend federal anti-discrimination protections to LGBTQ Americans
