Only about 7 percent of private sector workers are now unionized
The economics point here is pretty simple. You raise the price of something (labor through unionization) and people demand less of it. Sometimes the adjustment takes a long time, but it still occurs.
I recommend that people read the entire piece because John Fund does a great job of discussing the Employee Free Choice Act, where 30 percent of workers (some possibly because of union intimidation) can sign a statement that determines whether the entire company is unionized.