He was a member of the National Labor Relations Board, where he participated in or authored more than 125 opinions.
US President Donald Trump's choice for labour secretary has withdrawn from consideration on the eve of a long-delayed confirmation hearing.
Puzder, a food-chain owner, withdrew his nomination facing opposition from some Republican senators, which seemed to have made his confirmation hard.
Acosta was tapped after Trump's first nominee for the post, Andrew Puzder, withdrew under pressure over his business record and other past controversies in his personal life.
Puzder is CEO of the CKE restaurant chain, which includes Hardee's and Carl Jr's, and the idea of a fast food boss protecting workers' rights had raised eyebrows from the start.
Puzder needed support from at least 50 of the 52 Republicans in the Senate, as no Democrats or independents pledged to vote for him.
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"These are rumours and we've heard this tune before", said George Thompson, a spokesman for Puzder. It also came to light that Puzder had hired an undocumented immigrant as a maid, which didn't endear him to Republicans.
Acosta is an attorney who has worked in government in the past.
Senate Democratic Leader Chuck Schumer fanned the flames behind the opposition to Puzder in a statement Wednesday afternoon. Puzder said he had employed - and belatedly paid taxes on - a housekeeper not authorized to work in the United States.
The withdrawal comes after a week of scrutiny of decades-old abuse allegations from Puzder's ex-wife, which she has since retracted.
It recently emerged that his ex-wife had appeared in disguise as a victim of domestic violence in a 1990 episode of The Oprah Winfrey Show, titled High Class Battered Women.
Fierstein later recanted her accusations, and has defended Puzder's nomination.