Top Democratic donors in New York aren't happy with former Starbucks chairman and CEO Howard Schultz for saying he was "seriously thinking about running for president" as a "centrist independent."

As Schultz prepares to hold his book tour's first leg in New York just after he announced his presidential aspirations, Democratic financiers and strategists in the city are already criticizing his potential campaign.

"This is a pathetic vanity project, and Howard Schultz better start laying off the espresso," Robert Zimmerman, a leading party bundler, told CNBC on Monday. "I would not take lightly the inevitable hashtags popping up saying 'no Starbucks, no Schultz.'"

Some members of the New York donor class, including on Wall Street, are casting doubt on whether Schultz will even run. Some argue the move would cost the Democratic Party in its 2020 battle with President Donald Trump — and hurt the Starbucks brand.

The perceived potential for Schultz inadvertently helping Trump has already triggered some calls for action against the company, with social media hashtags such as "Boycott Starbucks" making the rounds on Twitter.

Nathan Lerner, co-founder of Draft Beto, a group looking to persuade former Rep. Beto O'Rourke to run for president, said in a tweet that he would be boycotting Starbucks. Lerner threatened to protest at Starbucks stores if Schultz were to run as an independent.

Tweet:

Orin Kramer, a New York hedge fund manager who backed Barack Obama and Hillary Clinton for president, believes that a Schultz independent candidacy will anger urban voters who dislike Trump and will lead to them walking away from buying their coffee at Starbucks.

"Wouldn't want to own Starbucks if he did it," Kramer said in an interview. "Starbucks is disproportionately in urban areas, and 40 percent of urban areas hate this guy [Trump]. "This guy is giving Trump a gift, and there is no contrary interpretation."