A conservative rally billed as an opportunity to "stand up to Occupy Wall Street extremists" fell flat on Thursday when it was co-opted by members of Occupy Wall Street.

Supporters of Americans for Prosperity, a Tea Party-esque group funded by the billionaire Koch brothers, gathered at the Rockefeller Center in midtown Manhattan to demonstrate against both Occupy Wall Street and President Obama.

But almost half of the sparse crowd were Occupy Wall Street protesters, smartly dressed and bearing signs parodying Americans for Prosperity's ultra-conservative message.

"My sign says: 'I'm dreaming of a white president, just like the ones we used to have,'" said Stan Williams, a labour organiser and member of the Occupy movement.

"There were some people, with my sign especially, who said why are you bringing race into it," said Williams, who is black. "But there were about five or six people who said: 'That's a great sign.'"

Warren Bancroft, co-founder of the satirical group Americans for Inequality, whose Facebook page describes the organisation as a "group of concerned citizens who cherish America's history of vast inequalities", was drawing approving nods from the Americans for Prosperity crowd as he loudly criticised the Occupy movement, arguing that "inequality plays a positive role".

"We're committed to reversing the narrative of inequality in this country," Bancroft said. "For the last year it's been dominated by the problems of inequality and the perils of inequality, but the truth is if you look at economic history, inequalities signal incentives to everyone in a dynamic market economy."

The dozen or so Americans for Prosperity supporters were almost matched in number by attendees pretending to be from Americans for Prosperity. Among other Occupy signs in the crowd were "Let them eat cake," and "I hate libraries", while a woman dressed in business attire had a piece of cardboard bearing the message "Every man for himself" – the quote attributed to Jesus Christ.

"There's a tradition of this," said a woman called Frances, an Occupy demonstrator who did not want to give her last name.

"There was a group called Billionaires for Bush that would dress up and they would come to demonstrations, and they would do a little skit about how they were billionaires and how they were very happy with the Bush tax cuts and the wars for oil.

"There's a tradition of street theatre and this was a little bit of street theatre."

Not all the parodists were necessarily affiliated with Occupy, however, with the Americans for Prosperity rally seemingly acting as a dog whistle for satire.

"I'm sick of the Occupy Wall Street protests … I'm sorry that I was born to a certain family and that I make more money than you. Maybe you should go and get a job," said a man who gave his name as John Wilker, who was clad in business attire and insisted he worked in the financial district.

"These are true patriots here. They're fighting the good fight to still make sure Americans such as myself are still given the opportunities that we've had for decades and decades and decades."

Wilker said he was not a part of the Occupy movement, but he and his companion Robert Stetson appeared to be engaging in the 'street theatre' Frances had mentioned.

"I think it's fine that the 1% earns far more than the 99%, that's how it should be. There should be a group of people that has worked hard, that has been able to set themselves apart. It's America," Stetson said. He and Wilker, like the Occupy infiltrators, were repeatedly questioned by the green T-shirt wearing Americans for Prosperity, rather derailing the rally and distracting from speakers.

The event had been organised as part of the group's "Failing Agenda" bus tour across the US. Americans for Prosperity has three coaches crossing the country, drawing attention to what it sees as Obama's failings on the economy, and Steve Lonegan, the organisation's New Jersey state director had described its stop outside the Rockefeller Center in New York as having an anti-Occupy theme.

But after Lonegan kicked off the rally just after 10.30am, summarising Obama's "failing agenda" and describing the need to "return ourselves to free market capitalism", bickering swiftly broke out in the crowd as Americans for Prosperity supporters sensed they were being infiltrated.

A red-haired Americans for Prosperity supporter was among the more vocal. "I built my own business, OK? Nobody gave it to me. I built it. What about you, who paid for your shoes? Who paid for your shoes?," she inquired as she tailed an Occupier bearing a "Let them eat cake" sign through the crowd.

"I was letting her know that my family, my mother – a single mother – had to support us," the red-haired woman told the Guardian. "That my mother took care of us and she was very poor. That when I was a little girl, we had to eat oatmeal, and our desert was a piece of toast with a little sugar on it. I let her know that my family had nothing and we boot-strapped our way up on our own."