I'd estimate the number not counted in the unemployment numbers to be between 1.5 million and 3.2 million, max.
9.784 million have left the labor force under Obama and are not counted as unemployed since he was elected 4.75 years ago. That's a lot of people, 75% more than left the labor force under George Bush. Not quite 9.5 million left under Bush, but that was over 8 full years.
Who are they who have left the labor force? And should any of them be counted as unemployed as many critics keep maintaining?
The people who should not be counted as unemployed from that total include the 1.1 million who retire every year, so subtract 5.2 million over the period, leaving 4.584 million. Those not in the labor force with a disability are up 1.4 million since 2008. Subtract them and that leaves 3.184 million.
As for the people who should be included in the unemployment number but aren't, they include the number leaving the labor force who wanted to work and searched for a job but were not counted as unemployed. But they were counted by the government. That number has increased by about 1 million since the beginning of the 2007 recession, as shown in the graph (h/t Mish). Then add in those not in the labor force who weren't discouraged workers but looked for work for other reasons and you add another 475,000. They weren't counted in the unemployment numbers either, but they were counted by the government.
So subtracting those 1.475 million from 3.184 million, you get 1.7 million unaccounted for who might or might not need to be included with those 1.475 million who perhaps should be. Many of those 1.7 million are probably like a lot of Americans who became sole proprietors in the aftermath of losing their regular jobs and involuntarily went into business for themselves, making lots less money than before in many instances, typically as contract employees and freelancers, supplementing their incomes from their savings and practicing frugality. The US Census Bureau might agree, having just reported here in May that between 2008 and 2011 alone the number of such "businesses" is up 1.2 million in the aggregate. That leaves you with a minimum expansion of the unemployed to 12.8 million from the current 11.3 million, and a maximum expansion to 14.5 million, but based on the Census data on sole proprietorships, I'll lean to the under.
The real unemployment rate would therefore be something a little higher than the current 7.3%, between 8.3% and 9.4%, but probably closer to 8.3%. I'll go with 8.6% unemployment based on an additional 1.975 million not in the labor force who could very well be in it.
That's almost 18% worse than the government says unemployment is right now, but based on what I see regularly from government estimates of things, that's routinely good enough for them.
After all, hasn't it been called "good enough for government work" for decades for a reason?