The Dow Jones industrial average was down 20 points at 12,795 in the first hour of trading. It spent most of the morning with the tiniest of gains.
The Standard & Poor's 500 index fell two points to 1,378. The Nasdaq composite lost five to 2,899.
Trading was expected to be light. The federal government and the U.S. bond market were closed for Veterans Day, and there were no economic reports scheduled for release.
The fiscal cliff refers to government spending cuts and tax increases that are scheduled to kick in at the beginning of the new year, unless a divided Congress and the White House can work out a compromise before then.
Some traders thought the small moves were nearly inevitable, because there has been no strongly positive or negative news about the economy or the possibility of a deal to avoid the fiscal cliff.
"Nothing good is going on," said Scott Freeze, president of Street One Financial in Huntingdon Valley, Pa. "Everything forward-looking remains dreary."
Last week, after voters returned a long-deadlocked divided government to Washington, the Dow dropped 434 points in two days and had one of its worst weeks of the year.
Even if lawmakers work out a compromise, as they usually do, the political fight until then is sure keep investors on edge, pitching the stock market back and forth until it's resolved. Economists say the cliff could cost the economy $800 billion and 3 million jobs and would plunge the U.S. back into recession.
President Barack Obama, a Democrat, and House Speaker John Boehner, a Republican, have spoken of compromise but appear to be taking firm stances on some issues. Obama will meet with labor representatives as well as other progressive groups Tuesday. He'll hold separate meetings with the business community Wednesday.
The effect on the markets has been widespread. Fiscal cliff worries were blamed for keeping a lid on European markets, which were trading mixed but nearly flat in the morning; and Asian markets, which ended mixed.
In Greece, lawmakers passed a new austerity budget, and the other countries that use the euro issued a "positive" report on the country. Greece is hoping the other euro countries will give it another $40 billion in bailout loans. The budget and the report are crucial steps.
Still, the new bailout isn't a sure thing: Some of the potential lenders must seek approval from their parliaments. Greece's main stock market index was down nearly 4 percent.
Freeze was among the underwhelmed. "At this point, all the Greek news is just noise," he said. "None of these bailouts really solve the underlying problem. Now if all of a sudden Spain became incredibly solvent and its unemployment rate went to 5 percent, then you'd see" a reason to buy.
Across Europe, there were other reminders that the debt crisis is far from solved. The Banking Association of Spain, a country where hundreds of thousands of borrowers have fallen behind on their mortgages, said it would curb evictions of some struggling homeowners. In Portugal, demonstrators planned protests against a scheduled visit from German Chancellor Angela Merkel. Germany helped bail out Portugal last year and insisted that the government there cut spending as a condition of getting the money, a sore point for some in Portugal.
Among U.S. stocks making big moves:
— Leucadia National announced it would buy the investment banking firm Jefferies Group. The Jefferies chief will run the combined company. Leucadia, a holding company with investments in an eclectic set of industries including beef processing and medical products, dropped nearly 4 percent, 96 cents, to $20.84. Jefferies soared 12 percent, $1.78 to $16.05.
— Sherwin-Williams, the paint company, jumped 4 percent after announcing it will buy Consorcio Comex, a privately held rival based in Mexico City. Its stock rose $6.17 to $147.01.
— Best Buy leapt after announcing it had named a new finance chief, a former executive of the upscale kitchen store Williams-Sonoma. Analysts hope the new numbers cruncher can help turn around a chain that has struggled to keep up with online competitors. Best Buy's stock rose 5 percent, or 81 cents, to $16.11.