Large numbers are being thrown around, which is confusing....
So, if the government borrows $700 billion for the bailout, let's say at 4.25% interest (a rate currently between the 10- and 30-year Treasury yield), taxpayers are on the hook for about $30 billion per year in interest. That adds roughly 1.1% to total federal spending, and is about $100 per person per year.
The bailout shouldn't actually cost $700 billion - the Treasury will be buying assets that are presumably worth something. Exactly how much they will ultimately be worth is a matter of great uncertainty, and we don't know yet how exactly, in practice, the Treasury will determine what it is willing to pay (i.e., how hard it will try to get a good deal). So, the $700 billion is an upper bound on the cost (unless, of course, they ask for more....).
That is about 5% of GDP. If we guesstimate (conservatively, I hope) that the full $700 billion is spent, and the Treasury loses 50%, we're talking 2.5% of GDP. So, the question is: in the absence of a bailout, would the additional, credit crunch-induced loss of output be larger than 2.5% of a year's GDP?