Mitsch, 62, a retired real estate broker from Merchantville, faces Democratic Sen. James Beach in a Camden County district with 2-1 Democratic registration. Political observers say Mitsch is a long shot.
But that hasn't stopped members of both parties from calling on him to drop out of the race before the Nov. 8 election.
"Phil Mitsch's remarks make him unfit for public office," said Rick Gorka, spokesman for the New Jersey State Republican Committee.
Republican Sen. Diane Allen of Burlington County's Seventh District said she had not seen Mitsch's tweet, but added that it sounded inappropriate.
"Anybody who would put anything like this out for real is not suited for public service," she said Wednesday. "It's not that it's outdated, it's wrong. I don't think it was ever the way we should have looked at women."
Democratic Assemblywoman Pamela Lampitt, who is running for reelection in the same district as Mitsch, was the first elected official to call for Mitsch's withdrawal from the race Friday when the tweets came to public light.
"These chauvinistic remarks about women are derogatory, they're harmful, and they're disgusting," she said. "I find the thought process to be just disgusting."
Mitsch says he won't step down. And Thomas Booth Jr., chairman of the Camden County GOP, supports him.
"Certainly it's a poor choice of words, and it's not words I would use to convey the concept," he said. "But I think it's Phil's first time in running for public office. He probably didn't appreciate the level of scrutiny that his comments might enjoy.