I think another issue is that our government has become so involved in regulating companies and businesses. When labor unions were bigger there was less government involvement in the way businesses were operated.
Unions get a bad rap in the American press and public in the modern day. Some of it is deserved, but much of it is just scapegoating, and most American simply don't remember a time where the worker had no voice. I would venture to guess that those who dislike unions would not voluntarily give up their minimum wage, their bathroom breaks, their maternity leave or their weekends, but I digress.
Another major factor in the demise of unionism in the US, in my opinion, is the changing nature of our economy. Unions started in two sectors in the 1800s: manufacturing and the trades. Many if not most of those jobs have left the United States for cheaper labor markets where there are--incidentally--no unions. As we have turned into a more technical and more service-oriented economy, it has been more difficult to organize the workforce, and as a result, union membership has declined along with their influence in government and policy.
I think accessteacher is on to something. My school is very pro-KEA and the teacher's union is always pushing for votes for candidates who don't always act in the best interest of every teacher, parent, and student. I am in the minority by not belonging to this teacher union because of the way the money is spent. I elect to have a little more control over where my hard-earned money goes. I can't imagine it would be much different for other union groups as well.
I wonder if part of the answer is that Unions in America have shown themselves to act undemocratically by trying to push for results that are not necessarily wanted or required by the individual members. I wonder too if part of the reason for the unpopularity of unions is because of their association with socialism, which is ideologically opposed to America's system of governance.
Americans are very proud of their democracy. Joining a union is a great choice for any American when it serves the purposes of labor groups collaborating in efforts to assert their rights and get their needs met. However, many American unions have gathered members and then used dues inappropriately. Therefore, many Americans exercise their right not to be involved with a union. Democracy offers the freedom of choice and many exercise their right to use their choice.
In my opinion, there are a couple of reasons.
First, Americans are more individualistic by nature and are therefore less likely than people from some other countries to join unions. They are also more likely to allow their governments to institute laws that make labor organizing difficult.
Second, there is the fact that states compete with one another for jobs. States that are "too" pro-union face the loss of jobs to less unionized states. This makes it less attractive to demand unionization.