The consensus of economists is that 563,000 non-farm payrolls were added in May.
Goldman Sachs economist Andrew Tilton said he expects to see a payroll number of 500,000. He expects 150,000 of that number to be private sector jobs. Last month, payrolls totaled 290,000 and the unemployment rate was 9.9. Tilton expects to see the unemployment rate drop to 9.7 percent.
"I would say jobs is the most important data, particularly private sector job growth," in the coming week, he said. "It doesn't have to be better than last time, but people are certainly expecting a three-digit gain."
Pierpont Securities chief economist Stephen Stanley said he expects to see about 230,000 new private sector jobs for May, up from 200,000 in April. He expects the overall number to be 640,000. The number of census workers should peak in May and turn negative in July and August.
Other data due in the coming week includes ISM manufacturing and ISM nonmanufacturing data, reported Tuesday and Thursday respectively. Those reports are also watched for clues about hiring trends in those sectors of the economy. ADP's employment report, released Wednesday is also a kind of early look at May's hiring activity. Weekly jobless claims are reported Thursday.
"The ISM manufacturing index, which is a pretty good bellwether for industrial activity, arguably may have peaked, so we may be seeing a little deceleration. That seems to be the message we're getting from some of the surveys we've seen this month, but it's still solid growth," said Tilton. He sees ISM slipping to 59 from 60.4 last month.
"The other thing that is important is we'll have the initial same store sales results for May (Thursday), which I think are widely thought to be a little softer, but obviously people will be interested in the details, along with auto sales (Wednesday). Those will give you a sense of how strong consumption was in May," he said. "We had a real consumer spending number for April which, was flat after a couple months of gains."
Tilton said a slowing in consumer activity would be consistent with Goldman's expectation of a softer second half. The firm's GDP forecast for the second half is currently 1.5 percent, down from 3 percent in the first half.
Other data due in the coming week includes construction spending, reported Tuesday; pending homes sales Wednesday and factory orders Thursday. Productivity and costs are also released Thursday.
Economists have been watching the unfolding of events in Europe, wary that its problems could be carried by the banking system to the U.S. Tilton said so far the economic impact would be modest.
"It's really credit that separates the mild or moderate scenarios from more severe scenarios," said Tilton in an interview Friday morning. "Market moves have definitely been more constructive in the last couple of days. You have seen some improvement in some credit spreads. They're still at quite elevated levels relative to a month ago, but at least incrementally on the week, they're a little better."
"The bottom line is there are some signs, if not easing, of at least stabilizing of some of the credit stresses. That is key because if banks continue to see higher funding costs and decide to pull back on the marginal loan or investment that ultimately represents tightening of financial conditions and that's bad for growth," he said.
Stanley said he does not expect the U.S. economy to take a serious hit from the European sovereign problem, despite its impact on markets this month. "The only way this really bleeds into the U.S. economy significantly is if the markets seize up again...I don't see that happening. People are reassessing the credit worthiness of European banks and I think that's a fair thing to do," he said.