Private-sector hiring hits 198,000 in February

After being hit hard by the economic downturn, small businesses are benefiting from the upswing in housing construction, he said. 

Construction has finally gone from a being major drag on the economy to a source of growth that will continue over the next couple of years, he said.

So, as fiscal headwinds wane into next year, Zandi expects the strength of the housing market to provide a much-needed lift for the economy. 

Construction added 21,000 jobs last month. 

Still, in a strong economy, employers would be adding about 300,000 jobs a month, he said. 

He expressed concerns that the $85 billion sequester that went into effect last week, combined with two years of steady spending cuts could weigh on the economy's ability to expand.  

"I'd be surprised if there were not some slowing in job growth as we make our way through the summer to the fall," he said in a call with reporters.

Job growth could drop to between 100,000 and 125,000 a month and gross domestic product could take a heavy hit of 1.5 percentage points from the budget cutting, he said.  

"Fiscal policy is a headwind to economic growth and it's blowing a lot harder," he said. 

Despite all the challenges, Zandi thinks the economy with "navigate through it" but there will be plenty of "hand-wringing around the impact."

The run up in stock prices is suggestive of how well the economy is doing. The Dow Jones industrial average shattered a record high on Tuesday. 

Overall, the service sector added 164,000 jobs last month. 

In a separate report on Tuesday, the Institute for Supply Management said the sector grew at its fastest pace in a year.