Shanghai stocks sold off 7 percent before being halted.
"China I think is one of the risks to the global economy," said Russ Koesterich, global chief investment stratgist at BlackRock. "I don't think the sell off of the Chinese stock market is fundamental for U.S. investors but it clearly affects sentiment."
Koesterich said some of the selling in Shanghai was technical, as restrictions on selling and other measures that were put in place during the summer selloff were being lifted.
He expects more China related sell offs in the future. "It's one of the things that's going to erupt over the next couple of years as the economy transitions. It's going to be more a source of volatility than one that mitigates it," he said.
Traders traditionally look to the first trading days of the year for clues about monthly and annual performance. There's the old Wall Street adage - 'so goes January, so goes the year.'
But Stovall said January has often been a rough month for stocks, and stocks rarely just move higher during the year. The S&P 500 has reached a lower level than where it started out the year 87 percent of the time since 1945, he said.
"One-third of all year-to-date lows were established in January," he said, noting the next highest month was October at 13 percent.
Stocks closed out a dramatic but ultimately, unsatisfying 2015, with the market selling off into the close on its final trading day, turning in a sluggish and mixed performance for the year.
The S&P 500 and Dow had their worst years since 2008. The S&P closed at 2,043, a decline of 0.7 percent, a second negative year since 2008, following on the even slimmer 0.003 percent decline of 2011. The Dow was down 2.2 percent at 17,425, but the Nasdaq was a bright spot, closing up 5.7 percent at 5007. A CNBC survey of 14 Wall Street strategists shows they expect relatively modest single-digit gains in 2016, with the S&P 500 expected to rise to an average 2,213.
Treasury yields were lower Monday as investors sought safety during the equities rout.
There's plenty for the bond market to consider this week including the Monday release of disappointing ISM manufacturing data, which came in at 48.2. There are also Fed meeting minutes and trade data on Wednesday, and the December employment report Friday. There are also about a half-dozen Fed speeches.
"It's the typical beginning of the month, reports coming in and people looking for a fresh start on a new year. January typically long term has been a relatively strong month, but in the more recent years, the returns haven't been that great," said Paul Hickey, co-founder of Bespoke. "Last year, we (stocks) were down 3 percent, and the year before down 3.5 percent, and 2013, up 5 percent. The last two years have been really weak so I don't think people are looking for too much."
Read MoreLots of fireworks but no grand finale for stocks