Greece's talks with creditors failed abruptly over the weekend, and its government shut down the financial system for six days to stop a run on the banks, as the European Central Bank capped the support it would provide Greek institutions. Greece has set a referendum for a public vote on the bailout measures next Sunday.
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The S&P 500 was down 43 points, or 2 percent to 2057, closing near its low of the day, and the Nasdaq lost 2.4 percent to 4958.
"There's a lot of complacency. I'm sure we'll have a more clear picture a week from today," said O'Rourke. "I think people should position themselves accordingly over the next week. If there's a negative event, you want to have confidence in what you own."
Strategists said the market reaction is negative, but it's still trading as if a positive outcome is still possible for Greece, such as a debt restructuring deal with European authorities and the IMF. The worst-case scenarios—Greece default, exit from the euro zone and contagion in other markets—are far from being priced in.
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"Only when we get a resolution do we find some stability and refocus our energy back on predicting when the Fed is going to hike rates and how strong growth is going to be," said Adams. "Today's response is a reaction to the complacency we saw over the past few weeks."
Jack Ablin, CIO of BMO Private Bank, said Tuesday's quarter end could be a factor in some of the selling, as fund managers shift their holdings. He said the market has traded as if investors expected an eleventh hour deal.
"I think we're probably overplaying it to the downside. It's hard to know how the Greek people will vote on something. My guess is they're getting a taste of default right now, and I think they'll be pushed to stay in the euro," he said.
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Before the Greece talks failed, the big focus of the week was Thursday's June employment report. There is also a heavy calendar of data on Wednesday, with ISM manufacturing and ADP.
"There's a lot of data coming out this week, and any strong number could turn our attention away from Greece," said Ablin.
Some strategists say the market's reaction is setting the stage for a buying opportunity.
Thomas Lee, founder of Fundstrat Global Advisors, said the situation would have to get a lot worse for the stock market to weaken significantly.
Lee said he does not think there will be contagion from Greece spreading to other European countries. "In some ways, this would reduce contagion because it's saying there's a limit to the brinkmanship," he said.
Citigroup U.S. equities strategist Tobias Levkovich, in a note, said that Citigroup investors said in a recent survey that they expect only a moderate impact from Greece's problems.
"Given more positive US economic developments (jobs, capital spending, home sales, durable goods orders, small business optimism, etc.); this should be seen as a buying opportunity," he wrote in a note Monday.
The U.S. Treasury market, traditionally the home base for investors seeking safety, saw buying Monday but yields came off the overnight lows. The 10-year was yielding 2.32 percent after touching a low of 2.29 percent.
"It's just a knee-jerk reaction to the headlines, and now people are cautious as we await the referendum," said Ian Lyngen, senior Treasury strategist at CRT Capital.