The Dow closed down 312.95 points, or 2.4 percent, at 12,932.73 â¿¿ its first close below 13,000 since Aug. 2.
The Standard & Poor's 500 index fell 33.86 points, or 2.4 percent, to 1,394. That was the broader index's first close below 1,400 since Aug. 30.
The Nasdaq composite index lost 74.64 points, or 2.5 percent, to 2.937.29.
U.S. stock futures had risen overnight after Obama cruised to victory. They turned sharply lower after the European forecasts and discouraging comments from Mario Draghi, president of the European Central Bank.
Now that the U.S. election has been resolved, it's natural for traders to focus on Europe's problems, said Peter Tchir, who manages the hedge fund TF Market Advisors.
What they're tuning in to, he said, is the failure of a major European summit last week and minimal progress on the issues that are holding the region back.
"People can only digest one or two stories at a time, and people had put Europe on the back burner" before the election, he said.
Obama's win followed a costly campaign that blanketed markets with uncertainty about possible changes to tax rates, government spending and other issues seen as crucial to the prospects of some industries and the broader economy.
As jitters about the election subsided, traders confronted an ugly reality: The so-called fiscal cliff, which will impose automatic tax increases and deep cuts to government spending at the end of the year unless the president and Congress reach a deal.
That's no easy task for a deadlocked government whose overall composition has barely changed â¿¿ a Democratic president and Senate and a Republican House.
If Congress and the White House don't reach a deal, the spending cuts and tax increases could total $800 billion next year. Some economists say that could push the economy back into recession.