Good news on employment would be good news for stocks, if not for the bond market.
Stock futures showed triple digit gains for the Dow when June payrolls came in at a surprising 195,000, but gains were constrained by a jump in bond yields in anticipation the Fed will move forward with its plan to pare back on quantitative easing sooner than some expected. The bond market is signaling that an increasing number of investors believe that will happen as early as September.
Stocks opened higher and turned negative in the first hour before trading higher again.
"Reality sunk in," said Art Cashin, director of floor operations at UBS, said during morning trading. "The key today will be bonds. The fact yields got up above 2.7 [percent] cut the legs out from under them, and they never recovered. Skeleton crews are on desks, and the reaction time is going to be slower." But later in the day, yields rose even higher, to 2.73 percent, and stocks ended the session with strong gains.
The dollar hit a three-year high against a basket of currencies, and gold fell more than 2.5 percent.
(Read More: Strong Jobs Report Is Gold's Nightmare)
The 10-year yield reached 2.73 percent for the first time since August, 2011, above its recent high of 2.66 percent.
The 195,000 nonfarm payrolls added in June was about 30,000 more than expected by economists, though the unemployment rate stayed at 7.6 percent. There were also revisions totaling 70,000 in April and May, which put jobs growth in those months above 190,000.
(Read More: Job Growth Posts Large Gain in June)
"This would be consistent with the Fed preparing the markets for a tapering of QE," said Moody's Analytics chief economist Mark Zandi. The Fed has been signaling that it will start to cut back on its $85-billion-a-month bond purchases by January if the economy improves, which has sent interest rates on a rapid run higher in the past several weeks.
"If job growth is 200,000, that would signal the end of QE and the beginning of rate hikes could be sooner than the time associated by the market," said Zandi. He noted that the six-month average has now moved to 202,000 jobs added a month, and there are an average 191,000 monthly jobs gains on a yearly basis. The average for the last three months is 196,000.
"As far as QE is concerned, the toothpaste is out of the tube, and they're not going to get it back in," said David Ader, chief Treasury strategist at CRT Captial. Ader said the selling started ahead of the 8:30 a.m. report, and could sell off next week when the government auctions 3- and 10-year notes and the 30-year bond.
"It's actually kind of relatively orderly. We were selling off in advance. We just added 10 to 15 basis points from where we were because this basically secures what the market was thinking," Ader said. "I don't see a lot of shock and awe. We were getting hints of this and here it is."
Rising rates have been a concern for stocks, which have been moving higher after an initial negative reaction to higher yields. Fed officials have been publicly talking down the rise in rates, assuring the markets it does not intend to raise short term rates sooner than expected. But Zandi said the strength of the jobs number could mean the unemployment rate will come down faster than the Fed expects.
The Fed has signaled it would start tapering when unemployment reaches 6.5 percent. Zandi said that may now be reached sooner, and the Fed could move to hiking rates in the spring of 2015, instead of the summer.
A concern is that rates will rise so much that economic activity is cut off, particularly in the important housing sector. Zandi said a 10-year yield of 2.75 percent sends mortgage rates closer to 5 percent for a 30-year conventional mortgage.
(Read More: Why Higher US Yields Should Cheer Investors)
"That would suck the wind out of refinancings, but it may not hurt sales because it will get fence sitters to move" ahead of higher rates, he said.
Dan Greenhaus, chief global strategist at BTIG, said stocks should be able to stand up to 2.7 percent yields, but he does expect choppy summer trading. "We've been very clear. These things happen from time to time. There are 34 instances, with the 10-year moving at a more rapid pace than this since 1990," he said. The 10-year has gained about 105 basis points in just a month.
"Stocks have moved higher nearly the entire time so the idea that higher interest rates are bad for the stock market is false on its face," he said. "That 1.60 (May 2 yield) was really an unnecessarily low level brought about by the spring swoon."
—By Patti Domm, CNBC executive news editor. Follow her on Twitter @pattidomm.