"Last time around, we were coming after the awful payroll number in March, so there was an expectation you were going to get a bounce back. Now, a lot of people are calling into question the strength of the data overall," said Tom Simons, money market economist at Jefferies. "I have heard people in the market talking about a 100,000 number, and a 300,000 number. There's a pretty wide range…. There's a lot of chatter two ways on the number, and I think it'll be reflected in the market."
Mesirow Financial chief economist Diane Swonk said she currently expects a September rate hike, but everything could change after Friday's number. She expects a below-consensus 205,000 jobs.
"As it is, I'm teetering on September, and we're going to make a call (Friday) on whether we push it back to December. The good auto sales were welcome news, but the data's been mixed. Anyway you cut it…it looks like it's going to be a lousy first half of the year. Right now we're not getting the bounce back we had last year," she said.
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Fed officials this past week have been a bit more glum in their economic assessments after Fed Chair Janet Yellen told markets May 22 that a rate hike is likely coming this year if the data is strong enough. Both Fed governors Lael Brainard and Daniel Tarullo warned of weakness in the economy, and Brainard commented on the potential for delaying rate hikes.
"The clock is ticking on September. Can the Fed achieve liftoff or not? Is it still doable? That's what they're signaling," Swonk said.
The market expectations for a rate hike have already been leaning toward December, while many economists have favored September based on the view that the Fed wants to get the process started. Either way, a jobs number that is out of line with expectations could sway rate hike expectations either way, and potentially take the markets with it.
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Traders may not have to wait long for Fed reaction to the number, since New York Fed President William Dudley speaks at 12:30 p.m. in Minneapolis. He will speak on the economy and take questions from the Economic Club of Minneapolis. Dudley's views are seen as closely aligned with those of Fed Chair Yellen.
"It could be a bit more buy on the rumor and sell on the news," said State Street Global Advisors chief investment strategist Michael Arone. The Treasury market's selloff in the past several sessions followed moves in German bunds, which were responding to European Central Bank President Mario Draghi's comments that the ECB will not react to rising bond yields.
Some strategists believe Thursday's bond moves could be signaling a near-term capitulation after the German 10-year breached 1 percent and then reversed course. The 10-year Treasury yield set a new eight-month high yield of 2.42 before reversing to 2.30 percent.
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"It's been a pretty volatile week. Rates have backed up on the 10-year decently here. If we get a strong report, this volatility could continue. If we get a strong report, the market concludes rate hikes sooner, rather than later. We could see a back up on the 10-year," said Arone.
He said the bond market may actually be sending a signal to the Fed. "The one thing, as it relates to bond market volatility, the Fed controls short-term interest rates and the Fed's been hemming and hawing—should we or shouldn't we for a while," Arone said. "The market might be saying, particularly on the long end: 'Let's move rates higher. Let's do policy normalization ourselves, and let the Fed catch up.' "
Arone said the Fed may ultimately have to be more aggressive in its hiking to keep up with the bond market.
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Cantor Fitzgerald rate strategist Justin Lederer said any rate move after the jobs number may be more muted after this week's extreme moves, and instead the action could be along the yield curve. "You could see a sizable move in the curve on a big number either way. If you do get a really strong number, I don't think June is in the cards. September could be," he said.
If the number is strong, Lederer said the yield curve could flatten, meaning the shorter end 2-year note yield could get closer to the 10-year and 30-year yields. That would signal a stronger economy and earlier Fed tightening. If the number is weak, the yield curve could steepen, signaling a weaker economy and easier Fed.
"We'll see how the payroll number will more or less shift the curve. If you get a stronger number, you could see a flatter curve with the front end taking more of the brunt of the selling and maybe breaking to higher yields. 2.42 (10-year yield) could be a strong support, especially if you see bunds go back to 1 percent," he said.
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As for the stock market, it rallied when the April jobs report (http://www.cnbc.com/id/102662083) was strong enough to signal the economy was not faltering, but weak enough to keep the Fed on hold for a while longer.
According to data and analysis firm Kensho, when the monthly jobs report misses by 25,000 or more, the dollar, gold and 10-year note yields are much more volatile than the major equity indexes. Since January 2010, 21 jobs reports have beaten by 25,000 or more jobs, and another 21 missed by the same.
Gold has been positive over 90 percent of the time when the jobs number was weaker than expected, while 10-year note yields have risen 85.7 percent of the time when the jobs number is greater than expected. The dollar index has risen 71.4 percent of the time when there is a large beat. The S&P 500, however, is positive 52.4 percent of the time when the number misses, with an average return of -0.4 percent.
Deutsche Bank economist Joseph LaVorgna expects to see Friday's nonfarm payrolls at 275,000, well above consensus. He said jobless claims and other anecdotal details, like a 5 percent jump in tax receipts, support the view that the jobs report could be better than expected.
"The trend in tax receipts has been remarkably steady and sturdy," he said.
He agrees with Arone that the bond market may be moving ahead of the Fed. "The interesting thing is what might get the Fed to move might not be the data. It might be financial market conditions…. If the market starts to think the Fed is going to lose control, that's going to get Yellen and some of the doves nervous," LaVorgna said.
Economists expect to see strength in construction jobs, but weakness in manufacturing in Friday's report.
"We may not have quantity, but we should have quality. The demand for college grads is picking up, and we're seeing demand for full-time hires in business services picking up," said Swonk. "We've seen a pretty dramatic decline in retail, leisure and hospitality. If we're going to be surprised on the upside, it will be we'll get more of those jobs. Manufacturing looks light. Construction looks good. We are at the point where we should see some movement in wages. We're hoping for it, but not calling for it."
Traders are watching the average hourly wages number closely for any signs of a pickup, which would be a signal of potential inflation. The Fed's dual mandate deals with employment and inflation and so far inflation has been disappointing.
What to Watch
The May employment report is released at 8:30 a.m. ET. Economists expect 225,000 nonfarm payrolls and an unchanged employment rate of 5.4 percent.
The Organization of the Petroleum Exporting Countries holds the 167th ordinary meeting of the conference in Vienna.
New York Fed President William Dudley speaks at 12:30 p.m. ET in Minneapolis. He will speak on the economy and implications for policy. He will take questions from the audience at the Economic Club of Minneapolis.
Consumer credit is released at 3 p.m.
The annual meeting of Wal-Mart's shareholders is at 8:30 a.m. in Fayetteville, Arkansas.
NBC's Gina Francolla contributed to this report.
Disclosure: NBCUniversal, parent of CNBC, is a minority investor in Kensho.