"I can't give tax cuts to the top two percent of Americans — 86 percent of that going to Americans making $1 million or more — and lower the deficit at the same time," he told CNBC. "I don't have the math."

However, Obama did leave the door open for tax cuts for the wealthy after the economic crisis subsides.

"Let's go ahead and move forward on what we've agreed to, which is tax relief for 97 percent of Americans," he said, adding, "at some point in the future, if we want to have discussions about furthering lowering tax rates, let's do so at a time when we can actually afford them."

Obama remains committed to extending the Bush-era tax cuts for individuals earning less than $200,000 a year and couples making less than $250,000 annually.

Sources tell The Hill that Senate Finance Chairman Max Baucus Max Sieben BaucusBottom line Bottom line The Hill's Morning Report - Presented by Facebook - George Floyd's death sparks protests, National Guard activation MORE (D-Mont.) could unveil his tax-cut proposal very soon.