How Big of a Problem is the Number of Uninsured in the US?

From the National Review Online (click link for whole article):

But the days of the uninsured as a potent issue for single-payer advocates may be numbered. There are two reasons.

First, it is becoming increasingly clear that the uninsured are over counted. For years, single-payer advocates have relied on the statistic produced by the Census Bureau, which now stands at 45 million uninsured. Yet a recent study by the Urban Institute — not exactly the free market’s best friend — claimed that the Census Bureau number was overstated by 4 million. Another study by the Department of Health and Human Services found it was too high by 9 million.