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 "It's not that it's outdated, it's wrong.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.
"Phil is a fantastic candidate; his ideas and his knowledge of the economy and his ideas for turning around the economy are innovative, they're fearless, they're bold, and I think that the citizens in Camden County appreciate that fresh perspective."
Asked about the state GOP's feeling that Mitsch is not suitable to be a state senator in the Sixth District, Booth said, "I think we'll let the voters decide that."
While Mitsch acknowledges making the "whores" tweet, he now says another Twitter exchange attributed to him was fabricated.
The Inquirer received a screen shot of a direct-message exchange from April between Mitsch and one of his followers in which Mitsch offered dating advice. Direct messages function like e-mail messages through Twitter and cannot be read by a user's other followers.
"tell your women they can't talk to you but they can moan," Mitsch wrote, according to the screen shot. "Life is far far less stressful when implementing this sex survival tip! lol"
In an interview last week with The Inquirer, Mitsch said the message was taken out of context. He said the comment about "moaning" simply meant that people should not damage their relationship by fighting.
"I definitely did not mean that sexually; I meant don't take the time to argue. . . . It's much easier in life to just agree to disagree rather than to argue," he said last Thursday.
He then said the message might have been sent by one of his associates at his office, who sometimes manage his Twitter account when he is traveling on business.
"Is it possible that I did? Yes, but I don't recall," he said.
At the Wednesday editorial board meeting, Mitsch said he could not find the direct messages on his account. He said he thinks the screen shot is a fake and an attempt to smear him.
"I did not post the tweets in question," he said. "They took phrases from tweets and rearranged them in order to make it appear - I feel deliberately and maliciously - that I was anti-female, and I have never acknowledged those tweets."
The follower who claims to have had the exchange with Mitsch is a 37-year-old man who did not know Mitsch but followed him because Mitsch offers financial and real estate advice. He now works for a Democratic politician in another state and said he did not want his name used for fear of losing his job.
He denies that he fabricated the exchange or baited Mitsch into making the statements, but he said the platform he used for Twitter did not save his sent direct messages, so he could provide no proof of his own comments to Mitsch.
Mitsch described his 67,000-plus tweets as riffs on finances, politics, life lessons, and relationship advice. He said he considers himself something of a Dear Abby and a motivational speaker.
Some of his tweets link to the blog on his website, phil-mitschforamerica.com, where he gives his explanations for the country's economic woes.
Some tweets read like motivational posters.
"Leadership Tip - great leaders do not control their followers. They lead them in the right direction," he wrote Monday.
Others are hard to characterize.
"Drinking draino and smoking dutch cleanser will only get a very few people through life," Mitsch wrote Sept. 1.
On Wednesday, Mitsch said he wanted voters to focus on his ideas for helping the economy, not his tweets, which he describes as sometimes infused with his "dry sense of humor."
Mitsch said New Jersey's 2 percent property-tax cap, which Gov. Christie signed into law last year, is "a total failure." He advocates an immediate cut to property taxes of 30 percent to 40 percent. Cuts to the state budget could pay for the plan, he said.
"Gov. Christie, of course I understand he doesn't have my business background and understand the economy the way I do, so I don't mean it as a personal attack on him, but he seems to be content just taking his foot and putting it lightly on the brake," Mitsch said. "But the car's still going to hit the wall and kill all the passengers in the car. What Phil Mitsch wants to do is, I want to take the pedal, push it through the floor onto the pavement, and stop."
Beach, who supported the property-tax-relief program, said Mitsch's plan was unreasonable.
"Obviously, he doesn't understand how the Legislature works," said Beach, 64, a senator since 2009. "You would have to get 21 senators to agree, you would have to get 41 Assembly people to agree, and the governor to agree. Or they're just words."
Contact staff writer Joelle Farrell at email@example.com, 856-779-3237 or @joellefarrell on Twitter.