Zandi said he is encouraged by the fact that the number has been firming in the past three months, at the same time business surveys show greater confidence. "Hopefully in last month's data we see another solid number, suggesting businesses are expanding operations more aggressively."
Economists say the latest sign of an improving job market was the fact that weekly jobless claims—at 284,000—were the lowest level in 8½ years. The four-week average fell to 303,000, the lowest since May 2007.
Read MoreAcross US job market, layoffs getting scarce
There was, however, a caveat around the claims number, since it followed two weeks where the number was elevated. Economists say it was most likely reflecting a return of auto workers after an annual early July furlough for retooling.
"People are a little confused by the auto plant layoffs in the first two weeks of July. It went up in the first two weeks of July, then it collapsed in the third week—kind of like it does every year," said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi. "I think the effect has probably passed. 284,000 is quite below 300,000. The evidence is compelling that the labor market is all but healed."
Barclays economists expect to see 225,000 nonfarm payrolls and an unemployment rate of 6 percent when July's employment report is released Aug. 1. There were 288,000 jobs added in June and the unemployment rate was 6.1 percent.
Job opening data have also been showing improvement, with 4.6 million job openings in May, the highest since March 2007. The ratio of unemployed workers is down to 2.1, the lowest since May 2008.