The phrase comes from Warren Buffett who used it in his definition of happiness.
Warren Edward Buffett (/ˈbʌfɨt/; born August 30, 1930) is an American business magnate, investor, and philanthropist. He is widely considered the most successful investor of the 20th century. Buffett is the primary shareholder, chairman and CEO of Berkshire Hathaway and consistently ranked among the world's wealthiest people. He was ranked as the world's wealthiest person in 2008 and as the third wealthiest person in 2011. In 2012, American magazine Time named Buffett one of the most influential people in the world.
Buffett used the phrase in an interview published in Fortune magazine in July 20, 1998:
The students and a few lucky guests were to be treated to a rare, public dialogue between the two richest businessmen in the solar system: Microsoft founder and CEO Bill Gates and Warren Buffett, chairman of Berkshire Hathaway Inc.
GATES: ... I was wondering how you define success, personally?
BUFFETT: I can certainly define happiness, because happy is what I am. I get to do what I like to do every single day of the year. I get to do it with people I like, and I don't have to associate with anybody who causes my stomach to churn. I tap-dance to work, and when I get there I think I'm supposed to lie on my back and paint the ceiling. It's tremendous fun. The only thing in my job that I don't like--and this just happens every three or four years--is that occasionally I have to fire somebody.
They say success is getting what you want and happiness is wanting what you get. I don't know which one applies in this case, but I do know I wouldn't be doing anything else. I'd advise you that when you go out to work, work for an organization of people you admire, because it will turn you on. I always worry about people who say, "I'm going to do this for ten years; I really don't like it very well. And then I'll do this...." That's a little like saving up sex for your old age. Not a very good idea.
I have turned down business deals that were otherwise decent deals because I didn't like the people I would have to work with. I didn't see any sense in pretending. To get involved with people who cause your stomach to churn--I say it's a lot like marrying for money. It's probably a bad idea under any circumstances, but it's absolutely crazy if you're already rich, right?
As Joel Brown comments:
It takes its meaning from the general happy tone of old Hollywood song and dance movies where the characters would break out into a happy song and do a tap dance.
The book you mention by Carol J. Loomis is about Buffett: Tap Dancing to Work: Warren Buffett on Practically Everything, 1966-2012: A Fortune Magazine Book.