"We're certainly aware of the ongoing conversations about ENDA," he said.
The American Civil Liberties Union, Lambda Legal and the National Gay and Lesbian Task Force are some of the most well-known groups to pull their support in recent days. They object to the current bill, they said, because its religious exemption is too broad.
The Human Rights Campaign is one notable group that has not withdrawn its endorsement.
The withdrawals followed a letter sent by religious leaders to President Barack Obama, asking him to carve out a religious exemption in a forthcoming executive order on non-discrimination for federal contractors. They cited the Senate bill and the Supreme Court's Hobby Lobby decision to make their case.
Earnest declined to comment Friday on whether Obama's executive order would include the requested religious exemption.