As a reminder, there are 2 major portions of this crisis. There's a credit crunch, in which banks don't know the true value of their assets and want to ensure they have the money to service their deposits and other liabilities, so they don't lend, and nobody can get money when they need it, even on a short term, highly reliable basis. The other portion is the recession, in which output is falling, reducing employment, consumption and leaving much of our capacity idle. These two issues are highly interrelated and worsen each other, but they're also separate. Specifically, it'll be almost impossible to fix the recession until the credit crunch is fixed, and the longer we let the recession go, the worse it makes the credit crisis because more and more people don't pay back loans due to loss of employment. So the credit crunch is very important to fix quickly.
As I mentioned, these are interrelated.
I'll start and say that Cochrane makes a VERY elementary mistake in his treatment of fiscal stimuli, one that Krugman and DeLong both tear him apart for.
However, he does have some good points on monetary stimulus, and, most relevant to here, he has interesting points on the liquidity crisis.
To make a very complex train of thought simple, he advocates that the US provide a monetary stimulus (increasing the money supply) while also easing the credit crunch by buying high quality corporate debt.
While corporations with junk ratings individually have quite high likelihoods of default during credit crises (default rates have historically been between 1 and 10%, and it's likely this will be higher than that range), as a whole, corporate America is probably likely to be able to pay off their debt. Needless to say, in this environment, interest rates are quite high. Purchasing this debt a) increases the money supply, avoiding recessionary deflation, b) provides LIQUIDITY quickly in the exact spot where banks won't do it but is still important to America, and c) buys a LOT more time to sort out the toxic assets on bank balance sheets.
Functionally, instead of trying to get banks to lend more, the government just does it for banks. In a few years, when everything has settled down, the government can dispose of the corporate bonds it has acquired, likely at a profit. This increases government revenue (we're running massive deficits) while minimizing inflation risks associated with quantitative easing, which is where the US buys back its own debt for cash to increase the money supply. The relative advantage is that in a few years, when the public is sick of holding money and government debt because it can finally stomach risk again, the government doesn't have to drastically increase interest rates to get money out of the system - it has high-yielding corporate debt to sell that can be attractive in markets without absurd risk aversion.
DeLong and Krugman tear apart Cochrane's fiscal stimulus mistake:
Lucas agrees with Cochrane on the liquidity crisis part: