Economists expect 225,000 nonfarm payrolls, an unchanged unemployment rate of 5.3 percent and an increase in average hourly wages of 0.2 percent, according to Thomson Reuters.
Besides jobs, there are a few other important economic reports in the coming week, including auto sales, personal income and spending, and ISM manufacturing data, all on Monday. There are also dozens of earnings from such sectors as health care, insurance, media and consumer staples.
Stocks were higher in the past week, but relatively subdued when compared to the wild action in currencies, fixed income and commodities markets, where some of the drama was clearly tied to shifting rate hike expectations.
For instance, when Friday's second-quarter employment cost index came in surprisingly weak, the dollar index plunged more than a percent before recovering. It also sent short-end rates lower, reversing the gains made by the two-year Treasury yield on a slightly hotter inflation print the day before. The two-year was yielding 0.66 percent late Friday, and had been as high as 0.75.
"If there's a decent size surprise (in jobs), I think we could have something that easily surpasses (the dollar move) we saw today. This is really about whether the Fed is going to be able to go in September, or are they able to go later. It could lead to a big sentiment shift," said Nordvig. "They almost have a window to go through. If they miss the window, there might not be any tightening at all."
Read More August may mean big things for markets and Fed
The odds of a September rate hike fell with the weak wage report, which showed the smallest gains going back to 1982. The Fed earlier in the week had assured markets it still wanted to boost rates this year, but that it was still watching the data in making its decision. The central bank also gave a nod to improving employment but it still has not seen the inflation it wants, though the Fed noted that it was "reasonably confident" inflation would move toward its 2 percent target.
"It looks like the week ahead is likely to give us this respite from thinking rates have to rise in the here and now ... but by the time we get to next Friday, and we see another strong jobs report, that respite is likely to come to a close," said Julian Emanuel, equity and derivatives strategist at UBS.
Economists in a CNBC survey were expecting a rate hike in September, by a slim majority, prior to the Fed's meeting in the past week. "I think the probability of a September move is lower, but it ultimately hinges on the next two jobs numbers. If payrolls grow more than 200,000 and closer to 250,000, I think all else being equal, they will move in September," said Mark Zandi, chief economist at Moody's Analytics.
He said the Fed would want to see average hourly wages rise, but some economists say it's not a condition of a rate increase.
Read MoreUS GDP a dud but gives Fed inflation glimmer it needs
Emanuel said the weak wage data could continue to influence markets in the week ahead.
"Basically, the Fed has continued to reinforce this idea that they are data dependent. ... This is data that continues to give the Fed more flexibility, where the market is now in the process of pushing its expectations from September to December," he said.
"From our point of view, what that says is we continue to be positive on the equity market but what we think you could see with this diminution of interest rate expectations is a bounce back in some of the areas that have been most adversely affected ... some of the interest rate-sensitive sectors like REITs and utilities. Those could be expected to underperform in the rising rate environment, but they are subject to very big bounce back possibilities."
Emanuel said the gains in those sectors could be quick and short-lived, if the market view on rates changes again. Utilities gained 1 percent on Friday and were up 6 percent for the month of July. The S&P 500 ended the week at 2,103, up 1.2 percent for the week, and nearly 2 percent higher for the month.