Formerly a lawyer and an academic affiliated with UCLA's School of Law, Sheinberg joined the legal department of Revue Productions (the production arm of MCA/Universal before divorcement of agency operation) in 1959 and within a decade had secured an executive position within MCA's TV division. Soon thereafter as a protege of Lew Wasserman, Sheinberg, at the age of 38, assumed his several important roles within the parent company.
When MCA was sold to Edgar Bronfman Jr in 1995, Sheinberg left and established his own production company, The Bubble Factory, with his two sons Jon and Bill Sheinberg. The first feature under this banner was 1996's "Flipper", a remake of the popular children's film and TV series of the 60s. The film sank at the box office but the Bubble Factory remained devoted to family fare and remakes. Projects in development early in 1997 included remakes of "Francis, the Talking Mule", Alfred Hitchcock's "Spellbound" and the 1932 Universal horror classic "The Mummy". Completed for release were a feature-length remake of the 60s military sitcom, "McHale's Navy" and "The Pest" (both 1997), a broad comedy starring John Leguizamo--who also co-wrote the story and co-produced with David Bar Katz--as a con man with a mastery of disguise.
Sheinberg is married to character actress Lorraine Gary, probably best known as Roy Scheider's wife in several of the "Jaws" films. They have long been active in numerous humanitarian causes and organizations.