I had never heard of "TBTF" until the crash of 2008, but apparently, the phrase had been bandied about at least since the 1984 collapse of Chicago's Continental Bank, a failure that motivated Ronald Reagan to abandon his free market principles and bail out the bank.
I myself prefer VoxEu's characterization of these institutions as "systemically risky." Let's use language that does not cloud the reality of our financial sector today. Is a "preowned" car any different than "used"? That's why I like "systemically risky." It does not obfuscate the fact that our financial system is as rickety (or even more rickety) than in 2008, when the sector collapsed in that terrifying global panic.
In 2009 testimony to Congress, Ben Bernanke shows he understands how the "systemically important" designation can lead to a risky identification with TBTF:
"Indeed, a more macroprudential focus is essential in light of the potential for explicit regulatory identification of systemically important firms to exacerbate the 'too big to fail' problem. Unless countervailing steps are taken, the belief by market participants that a particular firm is too big to fail, and that shareholders and creditors of the firm may be partially or fully protected from the consequences of a failure, has many undesirable effects. It materially weakens the incentive of shareholders and creditors of the firm to restrain the firm’s risk-taking, provides incentives for financial firms to become very large in order to be perceived as too big to fail, and creates an unlevel competitive playing field with smaller firms that may not be regarded as having implicit government support."
I know the Fed is working on developing resolution criteria to be used when a very large bank fails. But that doesn't change the fact that today's "systemically important" financial institutions remain as risky to our economy as the TBTF banks that dragged us off that cliff in 2008.
Some additional links:
A 2010 Mother Jones article on the influence of Wall Street lobbyists over regulatory legislation
FDIC 1997 report/book chapter on the failure of Continental Bank
Miami Herald article on Ben Bernanke's testimony before the Financial Crisis Inquiry Commission (09/03/10)
FCIC's report on the financial crisis