Bad jobs news, good stock news: Jim Paulsen

The April jobs report was not as strong as it first appeared, strategist Jim Paulsen said Friday.

"If you put in the revisions, it's a fairly back-to-back weak number again on average—below the 200,000 level with the negative revisions," Paulsen said on CNBC's "Squawk Box" moments after the employment numbers showed nonfarm payroll growth basically matching expectations for last month.

The Labor Department said the U.S. economy created 223,000 new jobs in April, with the unemployment rate falling to a seven-year low of 5.4 percent. But the already weak March payrolls number was revised lower to 85,000 from 126,000.

Read MoreRebound: U.S.economy adds 223K jobs in April

"I think people were bracing for a powerful number that might move up the Fed's exit strategy, and this sort of cooled that off," said Paulsen, Wells Capital Management's chief investment strategist. "I think that's why we're getting a rally" in the stock market.

Read MoreStocks jump 1% on 'Goldilocks' jobs report; Dow adds triple digits

Austan Goolsbee, former Obama administration chairman of the Council of Economic Advisers, provided a different interpretation.

"Now you're going to hear a lot of discussion again about the Fed," the University of Chicago Booth School of Business professor said. "Maybe [the March number] was just an aberration, and so the Fed will act."

Ahead of the jobs report, many economists were thinking the Federal Reserve might increase interest rates for the first time in nearly a decade in September, with outliers holding on to June as a possibility.

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But now, former Fed economist and ex-Romney economic policy adviser Kevin Hassett said forget June because the jobs report does not make him believe that the weak economic growth of the first quarter is going to pick up in the second quarter.

"We're not that far from still believing the second quarter is going to be very, very weak," said Hassett, who's with the American Enterprise Institute. "There's no way [Fed policymakers] are going to move in June" on rates.

Perhaps striking a balance between Hassett and Goolsbee, BofA Merrill Lynch's Ethan Harris said: "This is a Goldilocks number," referring to the fairly tale's not-too-hot, not-too-cold theme. "The economy is healthy but it's not booming, so we don't have to worry about the Fed in June."

Harris, co-head of global economic research at the financial services giant, added, "Here's the disappointing thing. ... This is the best we've got in the economy right now. The labor market is great; it's recovering."

"If it was just the labor market, the Fed should have hiked already," he continued. "The problem is the rest of the economy. We've had crummy exports, crummy cap ex, and mediocre consumer spending."

"We need to see the other data caught up to the jobs numbers," said Harris.

The slow economic growth in the first quarter is expected to be revised even lower based on recent sluggish data, when new figures are released later this month.