Actually the data is easy to find and is kept by the Bureau of Labor and Statistics. The way it breaks down is this
U1 unemployment...more than 15 weeks unemployed
U2 which is the percentage of the labor force that has lost a job permanently.
U3 (which is the official unemployment figure) Unemployed yet still actively looking
U4 which is the U3 data plus workers who stopped looking because they are "discouraged by economic conditions"
U5 which is U4 plus marginally attached workers.
U6 which is the real #. This is U5 plus part time workers who want to work full time but can't find work.
The U6 rate today is well over 14%. A far cry from the official 7.8%
Then there are those who simply opted to retire early because of economic conditions. Considering the baby boomer generation is retiring and makes up a significant demographic that is hard to measure precisely exactly who was forced to retire early and who had already planned to. But you can bet it is more than 14% when they are included. One of the other problems with the offical U3 data is that you are considered employed if you can only find work for as little a 1 hour per week.
The reality is the data is there if you know where to look. You assumption is sadly correct. The reality is that if we used the same metrics to measure unemployment as we did decades ago, the data would reflect closer to 20%. This is comparable to the late 1930's, about a decade into the depression. Which is why I believe that although there is not official economic definition for a depression, this period will likely go down in the history books as a depression.
Sadly a number of large US corporations announced thousands of additional layoffs just today as earnings are falling rapidly from a decline in top line revenue. The bottom line is the economy in the US is slowly grinding to a standstill. PMI data is terrible and durable good orders indicate we are bordering on slinding back into another recession. Polticians just have a way of making things look better than they are...especially in an election year.