This first chart helps put things in perspective. Note first that the household survey can be extremely volatile at times, and June's big employment decline has plenty of precedents. More often than not, a big move up or down in one month is followed by a reversal in the next month or two. Second, both surveys still appear to be in an uptrend, and both are saying that about 2 million private sector jobs have been added since early 2010. Taking an average of the six-month growth rate of the two surveys (next chart) yields an annualized growth rate of 1.3%. So it's reasonable to think that the economy is still growing, and that private sector jobs are probably increasing on average at a 1.3% annual rate, or about 120K per month. That's a very weak number, to be sure, but it is consistent with the fact that the unemployment rate has risen in the past two months and weekly claims for unemployment have been hovering at just over 400K per week (there has been no indication in the claims data to suggest a sudden and massive loss of 500K jobs in June). Conclusion: the economy is still growing, but slowly.
It's also of note that the decline in public sector payrolls to date was matched only by the 500K decline (bigger in percentage terms) in public sector payrolls that occurred from 1980 through 1983. This is a nasty shakeout for the public sector, but not without precedent. Happily, the economy enjoyed very strong growth from 1983 through 1989 after suffering through wrenching adjustments. I would like to think that all the bad news we are seeing these days (e.g., a painfully slow recovery, very high rates of unemployment) is setting us up for a shift to more growth-friendly fiscal policies, and it may come sooner rather than later given the looming issue of the debt ceiling.
UPDATE: reader "brodero" suggests that seasonal adjustment factors could have played a significant role in the June jobs weakness, just as seasonal factors have sent false signals with the weekly unemployment claims data. This would be one more justification for my decision to focus on the six-month trends in the data. Note this quote from High Frequency Economics:
In trying to explain the very weak June jobs report, Ian Shepherdson of High Frequency Economics examines the June seasonal factors. Because of summer jobs, the unadjusted number of June payrolls is always higher than the adjusted number. Shepherdson says the SA-NSA spread in private payrolls was -920K in June 2010; this year it was -1084K. The swing in the seasonal factor, -164K, was the biggest ever recorded (the data go back to 1947). He concludes: "Had last June's seasonal been used again, private payrolls would have been +221K."