Private vs. Federal Government Saving

We frequently hear about how: a) the U.S. trade deficits are unsustainable and demonstrate that we are living beyond our means, b) we've become a nation of debtors, partly at least because: c) Americans don't save.   

And yet the data above possibly suggest otherwise.  Personal saving is now close to an all-time high in nominal dollars at $673 billion, and has more than tripled since the fourth quarter of 2007 when it was $223.6 billion.  Meanwhile, negative federal government "saving" has increased by 5 times over that period from -$276 billion to -$1.35 trillion. 

So if there's a problem with a lack of saving, it's not the private sector that's the problem, it's the negative federal government saving of more than $1 trillion that's the real problem, no? At least for the last few years, the private sector looks pretty thrifty and responsible, and it's the federal government that looks pretty recklessly profligate.