The "nonmanufacturing service sector looks good. I think it's consistent with a plus-200,000 nonfarm payrolls and that should give the Fed the green light to hike in September," Cleveland said.
On Thursday, the August ISM nonmanufacturing index came in at 59.0, above expectations and a touch below the nearly 10-year high of 60.3 in July.
Other reports on Thursday, including continued low jobless claims levels and a narrowing of the trade deficit, continue to indicate a strengthening U.S. economy that can support liftoff as early as when the Fed meets Sept. 16-17.
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Analysts polled by Thomson Reuters expect a slight increase in nonfarm payrolls to 220,000 in August, with unemployment ticking down a tenth of a percentage point to 5.2 percent and average hourly earnings increasing at a steady 0.2 percent.
Importantly for many strategists, they said a decline in unemployment and an increase in wages could support the Fed's case for inflation, which has stayed below the 2 percent target.
Mark Luschini, chief investment strategist at Janney Montgomery Scott, expects 218,000 new jobs and said the market will likely only react strongly if the report shows "an unambiguously strong number."
"I think we'd need to see a number north of 250,000," he said.
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Stocks gave back sharp opening gains to close narrowly mixed Thursday as traders were on edge ahead of the labor report.
The Dow Jones industrial average ended up 23.38 points at 16,374.76, failing to break out of correction territory. The S&P 500 rose 2.27 points to 1,951.13, remaining out of correction. The Nasdaq composite fell 16.48 points to 4,733.50, also staying out of correction but erasing gains for 2015. All three major averages are negative year to date and on track for weekly losses of 1.5 percent or more.
The good U.S. economic environment reminds that as important as the jobs report is, a miss on expectations should not change the story much, many analysts said, especially since it comes on a Friday before the long Labor Day holiday weekend.
"Market action may be exaggerated tomorrow because (many traders are) absent from their desks," said Michael Arone, chief investment strategist of the intermediary business at State Street Global Advisors.
"The market's likely to get volatility in the next couple of weeks. I don't think we get that 'aha' clarity from the jobs report," he said.
In fact, historically over the past five years the market on average closes flat for the day after absorbing the jobs data, according to analysis using Kensho. The S&P 500 traded positive just about half the time with an average return of 0.01 percent over the last 67 jobs reports, the data showed.
Treasurys held fairly steady Thursday, with the 10-year yield little changed at 2.16 percent and the two-year yield at 0.69 percent.
"It's pricing in a very shallow path of rate hikes over the next couple of years," Cleveland said. "The rate hike is later according to markets and we get very few. The Fed seems to be telling us the opposite. We know they want to get going but they keep coming up with reasons to wait."
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Fed policymakers have said they are watching the impact of recent market volatility triggered by concerns over the economy in China.
Richmond Federal Reserve President Jeffrey Lacker is scheduled to speak on "The Case Against Further Delay" at a breakfast at 8:10 a.m ET. The voting member of the Federal Open Market Committee is a known hawk.
Market indicators of volatility and fear declined Thursday, Luschini noted, with gold settling lower for a second straight day at $1,124.50 an ounce, and the CBOE Volatility Index (.VIX) closing at 25.61, off recently elevated levels around 30. The VIX is widely considered the best gauge of fear in the market.
In another reprieve for markets, the mainland Chinese stock exchanges will also be closed Friday for a second straight day in commemoration of the end of World War II. The Hong Kong Stock Exchange will reopen Friday after a one-day holiday Thursday.
"The markets' breathing a collective sigh of relief on the back of that," Arone said.
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With no other major economic data or earnings releases due Friday, U.S. stocks will likely continue to take cues from oil prices. Crude oil briefly surged more than 4 percent Thursday before cutting gains to settle up 1 percent at $46.75 a barrel.
—CNBC's Gina Francolla contributed to this report.
Disclosure: NBCUniversal, parent of CNBC, is a minority investor in Kensho.