House Speaker Nancy Pelosi said blocking the measure was "an act of pure cruelty... leaving children and families out on the streets," in a tweet late Saturday
West Virginia Senator Shelley Moore Capito, ranking Republican on the Senate energy panel, said she is concerned that Biden's National Climate Adviser Gina McCarthy will have more control over policy than the EPA.
The new accusations surfaced after three women had accused Cuomo, 63, of sexually harassing them or making inappropriate remarks. He has denied any misconduct and pledged to cooperate with the review by James' office.
The measure also comes as lawmakers in 43 states have introduced legislation to place more limits on voting, according to the Brennan Center for Justice.
The tensions among Republicans have been exacerbated by a second showdown over an effort in Congress to override Trump's veto of a defense policy bill.