The cartoon published by the right-wing Post shows a police officer telling his colleague who had just shot a chimpanzee "they'll have to find someone else to write the next stimulus bill."
The leaders, including New York Governor David A Peterson, apparently believe that the cartoon compares Obama with the chimpanzee and thus evokes memories of racist past.
The inspiration for the cartoon obviously came from an incident in Connecticut on Tuesday where a police officer shot dead a 200-pound chimpanzee after it attacked and seriously injured the owner's friend and then tried to attack the officers after they had taken shelter in their cars.
Sean Delonas drew the cartoon. What added fuel to fire was that on the reverse side of the cartoon, a photograph of Obama signing the stimulus bill into law was published.
The Democratic leaders demanded explanation from the paper, saying that several people felt outraged by it.
Reports quoted journalists at the paper as saying that telephone callers protesting the cartoon had jammed its lines. The Post, however, stood behind the cartoon.
Editor-in-Chief of New York Post Col Allan said: "The cartoon is a clear parody of a current news event, to wit the shooting of a violent chimpanzee in Connecticut. It broadly mocks Washington's efforts to revive the economy."
"It would be very important for the Post to explain what cartoon was intended to portray," New York Governor said while replying to question as to whether it was racist.
"Obviously those types of associations are made. They do feed a kind of negative and stereotypical way that the people think. But I think if it's enough that people are raising the issue," he said.
Civil rights activist and black leader Al Sharpton said the cartoon was troubling at best given the history of racist attacks portraying African-Americans as being synonymous with monkeys.
"One has to question whether the cartoonist is making a less than casual reference to this," he said.
Some activist groups are planning to protest outside the Post's offices.
Senator Gillibrand, Democrat of New York, said he found the Post cartoon offensive and purposefully hurtful. He said this type of cartoon serves no productive role in the public discourse.
City Councilman Leroy G Comrie Jr, a Queens Democrat, called for a boycott of the newspaper. "To run such a violent, racist cartoon is an insult to all New Yorkers," he said in a statement.