"If you look at the relative employment compared to the potential, there's a very, very long way to go, " he added.
Hatzius explained that payrolls are only one input into the Fed's decision to taper its quantitative easing program, and although there are three more reports before September's Federal Open Market Committee meeting, strong numbers would not guarantee a tapering announcement at that time.
(Related: Job Growth Likely to Slow This Year: Goldman Sachs)
"Our base case is a December announcement of a taper and then an end to the program in Q3 2014," he said. "September is possible, but that is going to depend on the data. I think December is a little more likely."
Hatzius said that labor force participation is "partially depressed for cyclical reasons" and the trend of stabilization may occur over the next few years.
The report showed weakness in manufacturing and construction jobs, and although Hatzius expected manufacturing, he was surprised by the lag in construction over the past few months. "Generally things in the construction industry are doing better, so I still think it's probably a lag, but it's trailed a bit."
In the overall economy, Hatzius said that he expects gradual acceleration in GDP growth over the next few quarters. "Our expectation is third quarter, similar to where we are now, 2 percent. Then, a gradual acceleration, 2.5 percent in the fourth quarter. Then, 3 to 3.5 percent in 2014."
"As we get into 2014, we're going to talk about actual, good growth," he said.
_ By CNBC's Paul Toscano.
Follow him on Twitter and get the latest stories from "Squawk on the Street"