That is a mathematical anomoly. On the one hand we didn't lose nearly as many jobs as we expected, and yet, on the other hand, our unemployment rate went up a lot more than expected. How did this happen?
The two statistics are gathered in two totally different ways. When the labor department figures out how many jobs were gained or lost in any given month, bureaucrats survey a set of employers and ask them how many jobs they created and/or cut in the previous month. When the unemployment rate is measured, bureaucrats then call a set of households and ask that household who, of proper age, is or isn't working.
As such, both surveys can in fact be accurate, but they can also tell two totally different stories. For instance, it's very possible that the household survey shows a massive increase in unemployment because college grads have come home and found no work. (I showed a microcosm of this problem at Emory University) This phenomenon can also occur when a lot of very small business owners have to close up shop since one and two man operations are rarely surveyed in the jobs survey.
So, it's very possible that employers only cut 345,000 while the unemployment rate jumped much more than expected. It's very possible that while all this was happening millions of college grads entered the job market to find no jobs. Also, because times are tough, often, people are taking on second and third jobs. So, while job cuts may in fact have been smaller than normal, many more of these jobs could have been held by the same people over and over. Finally, the economy is likely keeping a lot more people in the workforce longer than they like. So, people that under better circumstances would be retired may still continue to be in the workforce also adding pressure to the unemployment rate.
Furthermore, while employers were reducing their cuts, they also may have been reducing the hours of the employees working. That isn't measured in the jobs numbers, though it is measured in a companion survey, average work week. In fact, that's exactly what happened. The average hourly work week fell by a fraction this month from last. Along with this, average wages climbed at their slowest pace in years. (even during recessions wages tend to still go up though their rise is often slowed)
In a reminder of the labor market's weakness, the length of the average work week eased to 33.1 hours from 33.2 in April. Average hourly earnings climbed to $18.54 from $18.52, putting earnings 3.1 percent above their year-ago level, the smallest 12-month gain since the period ended November 2005.
I generally don't like to hyperanalyze employment data. More often than not, employment data is hyperanalyzed so that someone can find an employment number buried within a pile of statistics that fits their world view. Then, they use that very number as the holy grail. I personally think the household survey, the one that measures unemployment rate, is the more accurate survey. The jobs survey has become the one that is more mainstream, and I so I will reference that more often than not when analyzing our employment situation.
These aren't necessarily normal times though. We have a very severe economic slump, however, we also have a very sophisticated economy. That economy became exponentially more sophisticated in the las ten plus years. Potential employees have a growing set of options and because they do, often the true nature of the economy requires a detailed analysis of all the numbers.