The "cliff" is tax increases and government spending cuts that take effect Jan. 1 unless Congress and the White House reach a deal to avert them. Economists have warned that the tax increases and spending cuts could eventually lead to a recession.
Shortly after Boehner spoke, Obama told reporters that a deal was "still a work in progress." Asked about Boehner's assertion that he was waiting to hear more from the president, Obama said only, "Merry Christmas."
The Dow drifted lower all day and was down 98 points at its low, just after 1 p.m. Then the Obama administration said that the president and Boehner would meet later Thursday at the White House.
Stocks still finished in the red. The Standard & Poor's 500 index dropped 9.03 points, or 0.6 percent, to 1,419.45. It was the first loss for the S&P in six days, tying its longest winning streak since early August.
The Nasdaq composite index dropped 21.65 points to 2,992.16.
The decline in stocks came despite the fourth straight weekly drop in applications for unemployment benefits. Applications fell 29,000 last week to 343,000, the second-lowest this year, the Labor Department reported.
Energy, health care and technology stocks fell the most, and consumer staples stocks were down only slightly. All 10 categories of stock in the S&P 500 index finished lower.
Best Buy shot up $1.94, or 16 percent, to $14.12 after a newspaper reported that the founder of the troubled electronics chain will make a bid of up to $6 billion for the company by the end of the week.
CVS Caremark climbed 96 cents, or 2 percent, to $48.50 after issuing a profit prediction for next year that was ahead of Wall Street expectations. The company also raised its dividend.
On Wednesday, the Dow declined for the first day in five. Stocks rallied in the afternoon after the Federal Reserve tied its pledge of super-low interest rates to an improvement in the unemployment rate, but the rally faded.
The Fed said it would hold interest rates super-low until the unemployment rate drops below 6.5 percent, a threshold the Fed believes may not be breached until the end of 2015. The rate is 7.7 percent today.
The Dow's close Wednesday of 13,245 put it within a point of its close on Election Day. After the election, stocks slid 5 percent as investors began to fret about the "fiscal cliff," but stocks have drifted back higher recently.
"I don't think anyone expected the markets to hold up this well as we get closer and closer to the deadline," said Randy Frederick, managing director of active trading and derivatives for Charles Schwab in Austin, Texas.
"Two possibilities: Either the markets are convinced that they'll reach some sort of agreement, or the markets don't care," he said.
David Steinberg, managing partner of DLS Capital outside Chicago, said that it was only natural for the market to pause after its run-up in recent weeks. He said that he did not think that the cliff would be a "grand event" for the market.
In the bond market, the yield on the benchmark 10-year U.S. Treasury note climbed to 1.73 percent from 1.70 percent late Wednesday.
Among individual stocks:
Google gained $5.14, or 0.7 percent, to $702.70 after releasing an updated map application for the iPhone. Google Maps came pre-loaded on previous iPhones but was dropped for the derided Apple Maps earlier this year.
SolarCity, which installs rooftop solar panels, began trading on the Nasdaq under the symbol SCTY. Shares were priced at $8 and shot to $11.79. Elon Musk, founder of PayPal and Tesla Motors, is the company's chairman.
Clearwire, a struggling provider of mobile Internet access services, jumped 41 cents, or 15 percent, to $3.16 in heavy trading after Sprint Nextel offered to buy out the minority shareholders of the company for $2.1 billion, giving Sprint total control.