I've written an article for OpenSource.com called APIs, not apps: What the future will be like when everyone can code, where I write about a coming future where programming ability is in the hands of everyone.
Despite this hype, I do think that coding will become a more widespread and routine skill in the years to come. Programmable technology will continue to pervade more parts of our life, computers will continue to become more accessible to a wider population, and the world will continue to become more complex. Understanding coding (and debugging) will naturally go with it.
These are areas where non-programmers can significantly boost their productivity by learning to code. This is different from everyone becoming a software engineer. When I say learn to code, I don't mean develop software professionally. Almost every adult has a driver's license, but only a minority are cab drivers or NASCAR racers.
Universal coding literacy doesn't increase the supply of web services so much as increase the sophistication in how web services are used. Programming—by which I mean being able to direct a computer to access data, organize it, and then make decisions based on it— will open up not only a popular ability to make more of online services, but also to demand more.