"If you look at the four-week moving average of initial claims, they've rarely gone below 300,000. The only times they have is in peaks of expansion," said Di Natale. Besides 2006, claims were under 300,000 in 1999, and the unemployment rate was much lower. "Those were very tight labor markets. It's very different now. You have a lot of slack in the labor market."
That labor slack has been a big concern for the Fed, and it shows up in the low participation rate—at 62.9 percent, near a post-recession low. There's also a high number of long-term unemployed, unchanged at 3.2 million people in July.
The Fed's forecast is that unemployment will reach a range of 5.4 to 5.7 percent in 2015 and 5.1 to 5.5 in 2016. The market has been watching the 6 percent level, since the central bank once targeted it as a level where it would begin to consider raising interest rates.
But Fed officials have said they have no target, and Fed Chair Janet Yellen has repeatedly emphasized her concerns about labor slack.
Di Natale said she expects the slack to diminish as full employment gets closer and the job market will achieve better equilibrium. She said data continues to show a mixed picture, where companies are not hiring but also not firing. Di Natale said government data on job openings shows the disparity.
Currently job openings as a share of employment is 3.4 percent, and it was 4 percent before the recession, she said. In 2009, it hit a low of 2.8 percent.
"This is just one side of the equation. On the layoff side it could indicate we get some modest increase in nonfarm payrolls, but the other side is hiring. ... It hasn't come back to where it was before the recession," she said.
July's slower gain of 209,000 nonfarm payrolls showed the economy is chugging along, and the labor market is improving, but economists also do not see it as strong enough to push the Fed to hike rates earlier than expected. Important to the central bank is the number of long-term unemployed, a group that accounts for 32.9 percent of the unemployed, and that number has dropped by 1.1 million over the past year.
A concern in markets has been that stronger data and signs of inflation mean the Fed will raise rates sooner than the second half of next year, the time frame expected by many economists.
The Fed ends tapering of its bond-buying program in October, and there's been lots of speculation about when the central bank would start to raise the fed funds rate.
Employment is one of the most critical components in its decision-making, and if it gets much stronger, economists say the Fed may have to rethink its timing. Some forecasters expect it to, and some Fed officials are calling for a swifter move toward the Fed's first rate hike.
—By CNBC's Patti Domm