”Why is it that in our personal lives, most of us realize that the world doesn’t owe us a living, yet in our public lives we have accepted an obligation to provide food, shelter, jobs, education, pensions, medical care, child support and other goods to every member of society?”

Because we decide it is in our rational self interest. For example, using public funds to vaccinate everyone against certain diseases leads to personal protection and a more productive work force. Similarly, providing an good educational opportunity to all children makes for a more productive society.

It's a liberating moment really when you realize that the world doesn't owe you a thing, and if it did, you wouldn't get it anyway in all probability. If you remember that the only thing that you owe the world, conversely, is honesty, you're free to look out for yourself.

Is this claim that most people recognize the world doesn't owe them anything true?

Limbaugh says that most liberals live like conservatives in their personal lives. Same point

This is the mistake that Rearden made. He worked hard and was moral in his work, but he accepted the moral code of the society around him when it came to the rest of life. What Dr. Kelly describes is people doing the same thing today.

We, or at least I, haven't accepted it. The problem is the limited means available to turn it around.