McCarthy said the first-quarter number is not worrisome since weakness was expected, and other data has been showing an improved outlook for the second quarter, which he thinks will grow at a 3.3 percent pace. "I don't think it's a new phase. It's a return to the phase we had entered into before the winter kind of derailed things. You are getting more of a critical mass. We are in an expansion phase at least for private-sector labor," he said.
Economists point to an important event in March where the job market went from recovering to expanding for the first time since the recession.
That was when private payrolls finally returned to their pre-recession peak—with the restoration of the more than 8.9 million jobs lost in the recession.
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"It took a little over six years to go from the early 2008 labor market peak to a new peak. That's a big milestone, but this cycle has been characterized by little mini cycles where payrolls accelerate and little mini cycles where payrolls decelerate," he said.
McCarthy said he does not expect the number to get substantially bigger until average hourly earnings start increasing more.
"Liftoff will come when you see average hourly earnings grow at a significantly faster pace," he said. Markets are honed in on wage growth because the Fed is focused on that. Wages are expected to rise 0.2 percent.
The jobs report is key because it is one of the most important data points for the Fed in policy making. But while April's employment report is important, the Fed will have the May report to also consider at its next policy meeting in June.
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Stocks meandered Thursday, after the Dow broke into record territory Wednesday. The Nasdaq was the standout, rising 12 points to close at 4,127, while the Dow was down 21 points at 16,558. The S&P 500 was off less than a point at 1,883.
The big mover was the bond market, where 30-year note yield temporarily slipped to 3.4 percent, the lowest since June 2013 and the 10-year note yield briefly broke below 2.60 percent, the bottom of a range it's been in since January.
Traders blamed short covering and repositioning but also some effect from the data, including construction spending number, which was 0.2 percent compared with expectations of 0.5 percent.