Another worry is the Jan. 25 Greek election, which could result in a party that has stated opposition to the country's bailout gaining more influence.
Analysts have said a soothing comment or two from the Fed in its minutes might help sentiment. But they are also looking at Friday's nonfarm payrolls, as an important catalyst. Besides ADP, a kind of warm-up act for the jobs report, there is also international trade data at 8:30 a.m.
"The best thing for the markets could be an employment number (Friday) that's far above consensus," said Emanuel. He said UBS is expecting 270,000 jobs in the government report Friday, down from the surprise 321,000 added in November.
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Besides the ADP data, markets will be watching oil inventory data Wednesday at 10:30 a.m. ET. Oil has reacted strongly to reports of higher-than-expected supply. On Tuesday, oil plunged again, with West Texas Intermediate crude futures for February, down $2.11 per barrel at $47.93, its lowest settle since April 2009.
Treasury yields also fell again Tuesday, with the 10-year yielding 1.94 percent in late trading.
"Oil is destructive for now," said Crescenzi. "In the end, it's a giant positive for the global economy and the U.S. economy. The disruptive element is what's driving trading activity."
Crescenzi said the 10-year yield has moved away from fair value. "We think it has moved beyond its fundamental value at these levels, but we recognize the global forces in play," he said. The 10-year yield has been moving lower in part on buying by investors who find U.S. yields more attractive than those in places like Europe or Japan.
"It would be surprising if it stayed below 2 percent this year," he said.
Emanuel said he expects the markets to stay volatile as some key hurdles are overcome, like the Greek election and ECB meeting, as well as the Fed's meeting Jan. 28.
"The volatility is going to be with us for at least another two weeks, with the potential of going into February," said Emanuel. "From the positioning point of view, it's shocking to us how much January of '15, looks like January of '14. People came in bullish stocks and very bearish bonds. The interest rate thesis is getting thrown out the window this week with the combination of concerns, which of course are helping along the selloff in oil."