The 175,000 nonfarm payrolls is consistent with the trend of the past four years, and of sluggish GDP growth of about 2 percent, said Mark Zandi, chief economist at Moody's Analytics.
"Nothing has changed" in terms of the Fed, said Zandi. "It's going to be September, October. The September meeting has a press conference. That would be a natural place to do it."
Gary Thayer, Wells Fargo Advisors chief macro strategist, however, does not believe the Fed will slow down purchases that soon because of sluggish hiring, and he does think the May employment report now means the process could be pushed back.
"We think we're just in a period where there could be move volatility, and we do expect the economy to improve and stocks to go higher," Thayer said. "After today, the expectations about tapering are going to be pushed forward a bit. I think people were worried the economy was getting too close to the point where the Fed would taper. and clearly we're not rushing to that point."
Canally said the actions of the Fed has encouraged the volatility, since many Fed officials have different views on when the Fed should pull back from the program. The "tapering" is also not an end to the program, and Fed officials have made it clear they could increase purchases again if the economy needs help. Canally said, however, it's not clear whether the Fed would start to unwind its program if it sees steady job growth at current levels, or it needs to see a level of 200,000, as suggested by Chicago Fed President Charles Evans.
(Read More: Greenspan: Taper Now, Even If Economy Isn't Ready)
"I think the best outcome for the markets might be to get some specifics from the Fed in the FOMC minutes. I think the jobs report was good. It's not great. It's not a game changer," he said. "If you're in the 200,000 camp, then you need a whiz bang jobs report in June."
Now with the jobs report out of the way, the Fed-sensitive markets will be watching the next Fed meeting, with a statement and Bernanke press briefing June 19.
In the meanwhile, markets are expected to remain volatile. "The thing we've identified, as being the big switch here is this bond market volatility that's been introduced, and that's made the market more volatile. This has taken the stock market rally since the beginning of the year, and put it in perspective. I think that's going to be the hallmark of the second half of the year. It's the end of the 30-year bull market in bonds," said Canally.
(Read More: Markets May Have Gone Too Far on Taper Talk: Plosser)
MKM's Michael Darda points out that average monthly job growth of 189,000 in 2013 is running slightly ahead of 2012's 183,000. He notes "despite massive hand-wringing about the effects of the sequester, average job gains this year are actually slightly stronger than the average of 2012, meaning the Fed, unlike the ECB, has likely offset the impact of austerity" on nominal GDP.