Are government job cuts undermining economic recovery?

Phil Izzo explains here that "[a]ccording to the [Labor Department's] household survey, which is where the unemployment rate
comes from, there are nearly 950,000 fewer people employed by the
government than there were when the recovery started in mid-2009. If
none of those people were counted as unemployed, the jobless rate would
be 7.1%, compared with the 7.7% rate reported on Friday. * * * No other sector comes close to those job losses over the same period.
Construction is in second worst place, but its 225,000 cuts are less
than a third of the government reductions. To be sure, construction and
other sectors performed worse during the depths of the recession, but no
area has had a worse recovery."