Even so, stocks had their best week since December, and the Nasdaq reached a fresh 13-year high. The Dow surged 2.3 percent to 16,154, and the S&P 500 rose 2.3 percent to 1,838, erasing all but a half of a percent of its recent decline.
With uncertainty about the debt ceiling removed with congressional votes and reassuring testimony from Fed Chair Janet Yellen this past week, the market's focus now shifts to the economy, and the wild card is the weather.
(Read more: Art Cashin: I'll be watching this next week)
Steven Wieting, global chief strategist at Citigroup Private Bank, said Wall Street may be underestimating the economic impact of the storms that have dumped snow and ice across the country and delivered record cold to some regions.
On Friday, Citigroup economists trimmed their first-quarter GDP growth outlook to 1 percent, from 1.5 to 2 percent.
"It doesn't last more than one to two quarters of impact," Wieting said. "This is very, very notable impact. To be clear, the markets are looking through this. I wouldn't get bearish on the U.S. economic outlook because of this."
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But Wieting expects the impact to show up in corporate profits, and earnings beats, which typically are far stronger in the first quarter, could be more muted. Fourth-quarter beats are generally less robust than those in the first quarter because companies tend to clear the deck and "kitchen sink" year-end reports, he said.
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Fourth-quarter earnings are so far up 11.3 percent for the S&P 500 companies, and 66 percent of the earnings reports beat expectations, according to Thomson Reuters.
All the talk about weaker economic data has sparked talk about whether the Fed will see the data as weak enough to pause its plan to taper bond-buying. In testimony this past week, Yellen said the central bank would continue with its plan unless the outlook changes notably, and that the weak jobs data may be the result of weather.
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UBS economist Drew Matus wrote in a note Friday that it will be difficult for the Fed to determine whether the economic data is being distorted by weather, even as late as its next meeting in March.
"Instead we will likely have to wait until the March data is released in April," he said. "The net result of this is that, in the absence of conclusive evidence, we believe the FOMC will continue with current policy and taper another $10 billion at the upcoming March FOMC meeting."
Economists expect the February jobs report will also show weather impact because the past week was the survey week for that report and storms disrupted activity up and down the East Coast. A CNBC survey showed economists expect a $50 billion hit from storms so far, though they forecast a rebound in activity.
"I would think things like restaurant sales are permanently lost," Wieting said. "Other things are merely delayed, so I just want to look at the difference between those two. I think the fact that incomes get hampered by this has broader spillover."
What else to watch
There is also an options expiration this week that traders are watching, and the market's rapid run has some expecting the market to take a pause. However, plenty of traders are gearing up for the market to take on its former highs, with the S&P in shooting distance of its 1,850 all-time high.
The market is closed for the President's Day holiday Monday.
"When you reopen, there's a mild bias that's negative," said Art Cashin, director of floor operations at UBS. "I believe it's options expiration that's helping both yesterday and today. The bias on the options expirations tends to be on the upside. We'll know that probably Tuesday and Wednesday."
Julian Emanuel, U.S. equity and derivative strategist at UBS, said the market could be ready to pause in the coming week as it rests from a rapid run off its lows. He is watching gold stocks, a play he favors in part based on the metal's outperforming of stocks when a new Fed chairman takes over.
(Read more: Gold bears running for cover)
He looked at a correlation between the S&P 500 and the price of gold and found that it "outperformed the S&P 500 because the Fed chair was always challenged by the market, and gold benefits in uncertain times.
"From our point of view, the rationale is gold outperforming in the months after the Fed transition," Emanuel said. "Janet Yellen may have made the markets happy this week, but there are communications challenges, especially when the data has been as sketchy as it's been since the beginning of the year. It's going to keep the communications a challenge. We think the gold stocks are poised to continue benefiting."
A number of gold companies report earnings in the coming week, including Eldorado Gold, Newmont Mining and Anglogold Ashanti.
Besides earnings, analysts will be watching as consumer brands companies convene in Florida for the Consumer Analysts Group of New York annual meeting Tuesday through Friday.