The U.S. economy added only 88,000 jobs last month, well below market expectations for a 200,000 increase. The jobless rate slipped to 7.6 percent from 7.7 percent.
(Read More: US Job Creation Plunges, but Rate Drops to 7.6%)
But as disappointing as the jobs report was, the March payrolls number didn't show much impact from the sequester, Hatzius said. Over the coming months, the labor market could lose about 20,000 or 30,000 jobs, and the impact "will probably go on for a while," the economist said.
Although jobs growth is softening, overall the news has been encouraging, Hatzius told CNBC, adding, "I would still say that even after the latest batch of weaker numbers."
Housing may be one reason for optimism about the broader U.S. economy. "I still think housing is recovering at an impressive and very pleasing clip," he said, noting that weaker construction employment in March was probably weather-related.
"In general, housing is moving up, that's providing a direct positive impulse to (gross domestic product) and there's probably a positive wealth effect," he said. "That's not really where the slowdown is going to be coming in the GDP numbers."