How much should we be willing to pay to save the US financial system ?

I would say much less than nothing. My sense is that there is a huge profit opportunity for any organization which can borrow for 3 months paying 0% interest and for which a standard deviation of wealth of $700 billion or so is no big deal.

That would be the US treasury and no one else.

There are many essentially equivalent ways to show that the US Treasury can make money out of Wall Street right now.

One is the good old ted spread now down to 2.36 percent. This means that, provided banks don't actually go bankrupt in the next three months, the Treasury could make a profit of 0.78 % or 0.79% of its investment in 3 months just by selling 3 month t-bills and loaning the money to banks.

Now of course the chance of the banks failing is positive, but it is not that high unless bankers are still irrationally optimistic. This is mainly because when deciding whether to loan to another bank or buy t-bills, banks have to consider that they will desperately need money exactly when their counterparty defaults and everyone wonders if they will too. This is not a problem for the Treasury, so loaning to banks should be significantly more attractive to the treasury than to other banks. That's a profit opportunity.

Another way of looking at it is that there are banks which have a high chance of failing if the treasury does nothing. Their shares currently have positive value. Their shareholders will have nothing if they fail. They should be willing to split the difference with the treasury -- another profit opportunity (or maybe the same one again)

Finally there is an increasing supply curve in shares of such banks -- their shares will be worth more if they recapitalize by selling shares. The treasury is big enough to act as a monopolist with a deal that it will buy shares at a price between their current value and their value if the bank recapitalizes.

I'd say that saving the banking system should cost the treasury negative tens of billions (at least).