"I really do think we're going to continue to see weather-related problems in the data. We're going to have to get a month of normal weather before we can tell what's going on," he said. "I think bottom line, the economy and the labor market are in better shape than the numbers show."
Diane Swonk, chief economist at Mesirow Financial, said the weather is clearly behind some elements of the report. For instance, there was a big drop in education workers, probably because of school closings, and there was also a big jump of 13,000 nonresidential specialty contractors, the type of workers that would fix things like frozen pipes and other storm damage.
But health care hiring was flat for a second month, and this is a change in trend, coincident with the Affordable Care Act. "It was recession proof. It's moderating and now. It's flat to down," said Swonk. "It's a stark shift. It's one we were expecting. They're not making their margins any longer. Economics has caught up to health care."
(Read more: Best growth in 10 years despite government headwinds)
Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi, found silver linings in the report. He noted that with annual benchmark revisions, there is more strength in the labor market than expected.
"The revision says March 2013 jobs are 369K higher than we thought," he wrote. "They also have found more jobs were created over the last 9 months of 2013. So today, the data show 2.322 million new jobs in 2013 ending December. An average of 193K per month. Then tack on the 113K new jobs in January 2014. The American economy is a veritable jobs-creating machine. 2.1 million in 2011, 2.2 million in 2012 and 2.3 million in 2013."
Rupkey also pointed out that the number of discouraged workers is not rising—837,000 was about the same as last year.
Besides cold weather, the drought in the west is also a concern. "The drought in California is certainly have a serious effect on their economy. So you'll be seeing it showing up in some of the economic data. I don't think it was a particularly big part of the story in the jobs numbers this month," said Jason Furman, chairman of the Council of Economic Advisers.
—By CNBC's Patti Domm. Follow her on Twitter