Many leaders in the Democratic Party are veering too far left and overpromising government programs that are not fiscally possible, Howard Schultz told CNBC on Tuesday.

Without naming names, Schultz said in a "Squawk Box" interview: "It concerns me that so many voices within the Democratic Party are going so far to the left. I say to myself, 'How are we going to pay for these things,' in terms of things like single payer [and] people espousing the fact that the government is going to give everyone a job. I don't think that's realistic."

"I think we got to get away from these falsehoods and start talking about the truth and not false promises" said Schultz, whose Monday announcement that he's stepping down as executive chairman of Starbucks is driving speculation that he may run for president in the 2020 election.

During the 2016 race for the Democratic presidential nomination against Hillary Clinton, Sen. Bernie Sanders, who described himself as a Democratic socialist, supported a single-payer "Medicare for all" policy on health care and other policies that his critics had said would be impossible to pay for.

"I think the greatest threat domestically to the country is this $21 trillion debt hanging over the cloud of America and future generations," Schultz said. "The only way we're going to get out of that is we've got to grow the economy, in my view, 4 percent or greater. And then we have to go after entitlements."