"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.
That could benefit consumer stocks, Coffin said. Consumer discretionary stocks in the S&P 500 (SPY) rose 6% since the start of the year. The sector includes companies like Starbucks (SBUX), Amazon (AMZN) and Nike (NKE).
"Incomes have slowed over the past several months as the work week has shortened," Coffin said. "But the broader trends in wages are very positive. We think the pressure on wages and payrolls above 200,000 jobs per month is enough to make the Fed [raise rates] this year, rather than later."
Whether that means a rate hike during the Fed's September or December meeting remains to be seen. The Fed meets again on June 16 to 17.