Obama has long opposed extending the cuts for families making more than $250,000 a year, but he gave in to GOP demands in 2010, when the cuts were up for renewal. They were extended two years.
The president also met with business leaders Wednesday to discuss the economy.
Obama is to meet Friday with Republican House Speaker John Boehner and the top Republican in the Senate, Mitch McConnell. They are expected to designate aides to begin the search for a compromise on the budget.
Boehner and McConnell have said they won't agree to raise tax rates for the wealthy. They have said they are willing to support raising overall tax revenue as part of a deal that also makes changes to the government's largest benefit programs.
There are ways to increase tax revenue from the wealthy without raising rates, including limiting tax deductions, but the path to compromise is unclear. Obama sidestepped a question about insisting on higher rates for the wealthy.
"I just want to emphasize I am open to new ideas if the Republican counterparts or some Democrats have a great idea for us to raise revenue, maintain progressivity, make sure the middle class isn't getting hit, reduces our deficit," he said.
On Wednesday, the Dow dropped 185.23 points, or 1.5 percent, to 12,570.95. The S&P fell 19.04 points, or 1.4 percent, to 1,355.49, and the Nasdaq composite declined 37.08 points, or 1.29 percent, to 2,846.81.
Indexes are still up on the year, though they have pared gains since reaching four-year highs. The S&P has fallen 7.5 percent since its Sept. 14 peak, and the Dow has fallen 7.6 percent, more than 1,000 points, since its Oct. 5 peak.
Among individual stocks, Abercrombie & Fitch, which sells teen clothes, bucked the trend of a declining market and was by far the best-performing stock in the S&P 500.