Worries that the Fed will keep hiking rates with a too weak economy is a recurring theme for the stock market.
Fed Chair Janet Yellen re-emphasized that economic data remain the most important signpost for the path of future hiking, after the central bank raised rates Wednesday.
For that reason, the ISM manufacturing survey and other reports in early January could play an outsized role for markets.
Read MoreArt Cashin: Why the Fed raised rates
According to UBS strategists, the ISM manufacturing survey, on the first trading day of the new year, could be a factor that helps determine the course of markets for the month of January.
For that matter, it could also influence performance for the year, if you believe the Wall Street adage — so goes January, so goes the year.
"Between the employment report in the first week of January and the ISM report, basically the first (trading days) of January are really going to set the tone for the entire month of January, and quite honestly looking to market history, it could very well set the whole tone for the year," said Julian Emanuel, equities and derivative strategist at UBS.
The Dow was down triple digits Thursday as oil prices sank and the dollar strengthened. Jobless claims data were strong. The Philadelphia Fed's gauge of manufacturing activity in the mid-Atlantic region fell to negative 5.9 from 1.9 in November.
"There's a clear dividing line between bulls and bears now. If you're bullish, you think the Fed is raising rates because the economy is good. It's very gradual and everything's going to be fine next year. That was yesterday's rally," said Peter Boockvar, chief market analyst at Lindsey Group.
"Then you get today, when you see the Philly Fed number, and you think 'Geez, she's embarking on this rate hike cycle in the seventh year of an economic expansion that's showing signs of strain. She's hiking interest rates, when global growth is soft and manufacturing is in recession. She's raising interest rates and she wants to do it four times this year.'"
Read MoreWhat's next for stocks after the Fed: Pisani
The December ISM survey will be especially important after it was surprisingly weak in November, falling to 48.6 percent, under 50 for the first time in three years. A reading under 50 signals contraction, and to many on Wall Street it reinforced what they were already seeing in other data — a manufacturing recession.
Boockvar said the bullish argument is that manufacturing is just a small part of the economy. "It's all these numbers. There's a lot of service businesses that do business with manufacturers, and the ISM services hasn't been that great either. She picked a fine time to raise rates."
Read MoreStocks ready for 'rip your face off' rally
But Emanuel said the emphasis on an under 50 reading is overblown, and if ISM recovers, it could be a positive for stocks. He said history shows that real recessions do not occur until the ISM hits 45.
"The last time it dipped below the 50 level was November 2012 and it was the mother of all buying opportunities," he said.
Emanuel said a recovery in the ISM would signal that the beaten-down industrials and sectors tied to manufacturing could start to recover, broadening the market's leadership. He said the market, now "long in the tooth," needs a broader group of leaders to reach new highs.
"When we look at the first half, if the data falls into place we think the market could overshoot in the first half. We suggested you could see a trade up to 2,500 in the S&P in the first half. That's contingent on the public's embracing the message from the Fed," said Emanuel.
Read MoreFed could pump some new life into aging bull
Many market pundits gave the U.S. central bank fairly high marks for its communications Wednesday, and stocks and global equities rallied as a result. Many traders had expected the Fed decision to clear the way for a year-end Santa rally, which clearly hit a bump Thursday.