And Rep. Eric Cantor, R-Virginia, the second ranking House Republican, refused to commit to bringing up the legislation. He said that he and fellow Republican leaders "will review it" if the Senate passes it.
House Democratic Leader, Nancy Pelosi, said the measure would still pass the House despite Boehner's opposition because most Democrats would support it.
"All we need is maybe 20 Republicans and we can pass the bill," she said on MSNBC Sunday.
Chad Griffin, president of the LGBT activist group Human Rights Campaign, had harsh words for Boehner.
"The speaker, of all people, should certainly know what it's like to go to work every day afraid of being fired. Instead of letting the far right trample him again, it's time for Speaker Boehner to stand with the majority of everyday Republican voters and support ENDA," Griffin said.
The conservative political organization Heritage Action put out a notice to all Republican lawmakers recommending a no vote. Its scorecards are threatening assessments of lawmakers who fear a primary challenger or are in need of the outside group's influx of campaign cash.
Heritage Action says the bill "raises serious religious liberty concerns" and would "potentially discourage job creation."
Family Research Council President Tony Perkins also slammed ENDA.
"Can you imagine walking into your child's classroom and meeting a teacher dressed in drag? Neither can most Americans. But unfortunately, that's just one of the many consequences of adopting a law as dangerous as this one," he wrote in a blog post Friday.
"Preschools, day care centers, summer camps, religious chains like Hobby Lobby or Chick-fil-A -- they'll all be subject to the law, regardless of their personal beliefs and workplace standards," Perkins said.
An exemption for religious organizations is included in the bill, but some want the religious protection extended to secular businesses, which ENDA proponents say would gut the entire bill. Employers with fewer than 15 employees would also be exempted from the law.
Heads of major businesses have come out in support of the law, including Tim Cook, Apple's CEO, who wrote an op-ed Monday in the Wall Street Journal.
"So long as the law remains silent on the workplace rights of gay and lesbian Americans, we as a nation are effectively consenting to discrimination against them," he wrote. "We urge senators to support the Employment Nondiscrimination Act, and we challenge the House of Representatives to bring it to the floor for a vote."
Twenty-one states currently have laws on the books protecting lesbian and gay workers from discrimination and 17 states protect transgender workers, according to the Human Rights Campaign. The federal statute would create protections in all states and the District of Columbia.