The reaction has been back-and-forth in a very narrow range, but with very typical volume for NFP (in other words, traders are clearly trading... they're just conflicted). Why the conflict? Sure, at 559k vs 650k f'cast, the number was weaker than expected, but it was nonetheless a big step up from last month's 278k. By the time we consider seasonal distortions, the data is actually fairly strong.
MBA Chief Economist Mike Fratantoni shared a good observation about the NSA (not seasonally adjusted) numbers, saying "in both April and May, the monthly NSA increase was closer to 1 million. The seasonal adjustment is likely significantly complicated by the huge swings in employment over the past year. The NSA changes may be reflecting stronger underlying growth than the headline numbers suggest."
In addition, we should also consider this data is actually fairly old (NFP data was collected almost an entire month ago and since then, Jobless claims data suggests things have been improving more rapidly). Bottom line: the jobs report was a bit stronger than it looks at first glance, but so far, bonds don't seem to mind! If anything, both stocks and bonds are telling us that the market needed to see an even bigger number in order to maintain a defensive stance about Fed tapering prospects (ongoing Fed support = rising tide that benefits both stocks and bonds).