Obama's health care savings estimate off by a factor of 4

In his speech last night on health care, President Obama stated:

Reducing the waste and inefficiency in Medicare and Medicaid will pay for most of this plan.

I've done a simple calculation to check the accuracy of this statement.  The Congressional Budget Office estimates Obamacare will add $1 trillion to the national debt over the next 10 years.  In 2007-2008 there were 43 million and 49 million Medicare and Medicaid recipients, respectively.  The average annual administrative cost per person in Medicare was $509 in 2005 (the most recent data available), and we can assume a similar number for Medicaid.  If Obamacare succeeds beyond everyone's wildest dreams, in fact beyond what is physically possible, and reduces waste and inefficiency in Medicare and Medicaid by 100%, it will save $509 x (43 + 49 million) * 10 years = $468 billion over 10 years.  That's less than half the net cost of Obamacare.

A more reasonable estimate would be a waste reduction of 50%*, which would mean $234 billion in savings.  That's less than 1/4 the net cost of Obamacare.  Also note that the CBO's $1 trillion estimate already takes into account the cost savings proposed in H.R. 3200, so in reality Obama's savings estimate is off by a far greater amount.  There is no way reducing waste and inefficiency in Medicare and Medicaid could pay for Obamacare.

*Many conservatives argue there will be no savings at all.