Blame globalization for that, not absurd CEO pay. There are now many people that are willing to do what were blue collar and middle class jobs for much, much less, and they'll do it just as well. There are fewer and fewer natural reasons for companies to pay US workers the premium they command.
At least partly because it's a very rare and specialized skillset - you basically have to have run large divisions in large companies or other large organizations, or been the CEO of a smaller company to be considered for the top spot at one of the large companies that pay these outlandish sums.
A good CEO can be worth an incredible amount of money to a large company, which is why they command such amazing pay. Just think, how much is it worth to Apple to have Steve Jobs as CEO vs. someone else? His leadership helped add hundreds of billions of dollars to their market cap. Naturally, the owners of the company are going to be willing to pay him a lot to help keep his interest.
CEOs are a popular scapegoat because they're easy to identify and their rewards are outsized, but they're not the actual problem, and it's counterproductive to focus on their compensation.