I tend to think that Fannie Mae and Freddie Mac are treated as too big too fail, what would happen if one of them did fail and the ramifications are debateable. Thus what is the definition of TBTF is the question. I guess its whether or not the govt would step in to save them or not. Presently F & F are TBTF, however it doesnt necessarily have to be that way, simply a change in the White House could change all of that.
The reason why AIG was saved and also TARP was instituted was to calm the financial markets which had frozen up. Its not that AIG and Citibank are too big to fail, but rather our country was panicked and believed capitalism had failed.
Can Citibank be allowed to fail and our financial markets do OK? Sure, however it wont be allowed to fail at a time when our Govt has the perception that our whole banking system is failing. In other words our banking system was not failing because Citibank or AIG was failing in and of themselves; however at the time they were failing so was the rest of our whole banking system and that is why they were bailed out..... as a part of a bailout of the whole system which was done by attempting to calm the market.
There is no institution, except for perhaps F & F that are too big to fail, although if we are in a crises our govt will once again step in as it should.