The government exceeded the current debt ceiling of $14.29 trillion in May, but the Treasury Department implemented special measures delaying the date of a potential default until Aug. 2.
"(T)his is something that we shouldn't be toying with," Obama said in response to a question about the debt ceiling at the White House event, moderated by Twitter co-founder Jack Dorsey.
If Congress fails to act, the president said, "then the Treasury will run out of money. It will not be able to pay the bills that are owing, and potentially the entire world capital markets could decide, you know what, the full faith and credit of the United States doesn't mean anything."
"And so our credit could be downgraded, interest rates could go drastically up, and it could cause a whole new spiral into a second recession, or worse," Obama said.
Democrats and Republicans have been engaged in often contentious negotiations in pursuit of agreement on a plan that would increase the debt ceiling while reducing the budget deficit.
Obama returned Wednesday to his theme that curbing the deficit will entail not only spending cuts, but revenue increases, which many Republicans have ruled out.
"I think that for us to say that millionaires and billionaires can go back to the tax rate that existed when Bill Clinton was president ... that makes sense to me," he said in response to a question about his proposal to limit deductions for high earners.
"(W)e actually now have the lowest tax rates since the 1950s," the president pointed out.
Obama said he is not willing to cut essential health and education programs simply to preserve tax breaks for the wealthy.