I was thinking about this statement and how it has changed in meaning over time but remains relatively constant in purposed solution. I think this concept can be thought of in two parts:
Early "Too Big To Fail": I think this would be epitomized by John Kenneth Galbraith's 1952 book American Capitalism: The Concept of Countervailing Power. My reading of his arguments were that the industrial revolution gave away to oligopolies who broke the previous laws of markets and competition. Now oligopolies, like GM and Ford, were so big and powerful that the only way consumers and labor could share in prosperity was if they became institutionalized in democratic government. I think this version had solid footing into the 1970's, perhaps even into the 1980's. Diagnosis: Firm's became so big, they were not capable of anything except utter dominance of the marketplace. Solution: Heavy and direct government intervention into the management of these firms.
Modern "Too Big To Fail": This is the argument we are confronting now, which I think started to become a more dominant view with the Savings & Loan's crisis of the 1980's, along with the struggles of the oligopolies confronted with Japanese competition. Diagnosis: Firms, like Ford and GM are so big that their failure is unaccpetable because their extended reach into the economy would have too large of a spillover effect. Solution: Heavy and direct government intervention into the management of these firms.