So the number of Americans without insurance is actually closer to 36 million
Getting back to Obama's statement, he said, "Nearly 46 million Americans don't have health insurance coverage today." That is the most recent number for the U.S. Census available, but he messes it up in one way that would tend to overcount the uninsured and in another way that would tend to undercount them.
It's an overcount because it counts noncitizens. Take out the 9.7 million noncitizens and the actual number is closer to 36 million.
It's an undercount because it's old data from when the economy was doing much better, and it was for people who were uninsured for a whole year. If you wanted to look at numbers just for "today," the number would likely be higher, but by how much we can't say. (The Department of Health and Human Services survey found that there were 57.7 million uninsured at some point during the first half of 2008, but we couldn't find a breakout for noncitizens.)
PolitiFact | Number of those without health insurance about 46 million[/url