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Next up for market: Jobless claims

Jobless claims data Thursday could provide another shot of encouragement for market bulls who are looking for improving economic news to drive stocks higher.

All economic reports, and particularly jobs-related numbers, are under scrutiny as traders watch to see if the malaise of the winter economy had to do with extreme bad weather or something else.

ADP payroll data Wednesday encouraged traders who expect the March employment report Friday to come in at the consensus forecast of 200,000 or even better. ADP reported 191,000 private sector jobs were added. It follows on Tuesday's surprisingly strong auto sales.

Traders on the floor of the New York Stock Exchange.
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Traders on the floor of the New York Stock Exchange.

Jobless claims are expected to rise slightly from last week, to 320,000, when they are reported at 8:30 a.m. ET. Trade data are also expected at 8:30 a.m., and ISM nonmanufacturing data are set to be released at 10 a.m. ISM will be especially watched for what it says about service sector hiring.

"I think the economy is getting better. I think today's number was mostly about a rebound to the trend we were on before the winter," said John Ryding, chief economist of RDQ Economics.

Read MoreSpring thaw? Private sector ramps up job creation

"Claims numbers are very low," Ryding said. "I think the message is very clear. Layoffs are very low. They are at expansion norms. Not many people are being laid off but that's not the part of the labor market that's not functioning. The part of the labor market that's not functioning is fitting the unemployed into the job market."

The Dow on Wednesday rose 40 to 16,573, just 3 points shy of its record, and the S&P 500 climbed 5 points to 1,890, its eighth record close this year. The Nasdaq gained 8 to 4,276. The S&P 400 midcap index and the Dow Transports both hit new all-time highs.

"For right now, I think it still pays to be cautiously bullish, and it's possible fundamentals catch up with the market," said Jack Ablin, CIO of BMO Private Bank. "It's a funny market but from what I see, there's a couple of warning signs but not too many danger signals."

Read MoreHFT debate may claim VIrtu IPO as victim

Ablin said high valuations and a turn in geopolitical events would be the types of things that could make the market stumble.

"To the extent that March weather was better than February, are we going to see better numbers as a result?" Ablin said. "We're seeing a lot of business really has been pushed back. Right now, analysts expectations for Q1 are so meager but for the rest of the year, they're pretty robust."

Stocks have been moving higher ahead of the week's big number—Friday's nonfarm payrolls.

Ryding said he expects to see 195,000 jobs and an unemployment rate of 6.6 percent, down from 6.7 percent in February. He said, however, there could be a case for a bigger number, if the bounce back from the winter is greater than expected. One deviation could push the number to 280,000 or so.

Ryding also points out an interesting coincidence that popped up in March 1994, and then again, 10 years later in 2004. In both those years, the Fed was moving to tighten and in both years, March's jobs number surprised to the upside in a big way, with 456,000 jobs added in March 1994.

Read MoreCashin: How traders are betting on the jobs number

This year, the Fed is moving to taper its quantitative easing program and talking about a time when it will begin to push rates higher.

"We are not forecasting but musing on the potential for history to repeat itself again," Ryding said.

Besides U.S. data, markets are focused on the European Central Bank meeting. The ECB has said it could increase stimulus and some traders expect to see that at this meeting.

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