Austan Goolsbee, the former chairman of President Obama's Council of Economic Advisers, said Friday that the just-released jobs report is a "punch to the gut" and suggested that the tepid number of new jobs added in March is a result of the sequester cuts.

"Look: We all over-shot it," Goolsbee said on CNBC, referring to the projections of much higher job gains. "This is a punch to the gut. This is not a good number. And I think now you're going to interestingly start seeing a lot of discussion about maybe the sequester's a bigger deal than people thought it was."

The jobs report showed the unemployment rate dropping a bit, to 7.6 percent. But the number of jobs created -- 88,000 -- was far less than expected, and a big reason the unemployment rate fell is because nearly half a million people dropped out of the workforce.

The March report comes just one month after a report hailed as one of the strongest in years, with 268,000 jobs created.

For more, see Ylan Q. Mui's recap.