"We did beat expectations, but when we talk about underlying strength [in the labor market], I still think we have quite a ways to go before we can talk about a robust hiring sector," said Lindsey Piegza, chief economist at Sterne Agee.
"I don"t think the Fed will hike rates sooner on one month of data," said UBS economist Sam Coffin.
Meanwhile, Piegza thinks the Fed will pull the trigger in 2016. "The Fed is going to be very persistent that they want to see continued strength in the labor market," she said. "We're talking about several consecutive months of job creation above 300,000 jobs. We"re still not at a pace where we can talk about a very robust employment sector."
Over the past three months, the economy created an average of 207,000 jobs, the Labor Department said.
Aside from the headline employment number, the Fed will also be watching wages, which rose 0.3% in May, compared to April's 0.1% increase.