We can not compare Greece with the US.This is a theoretical debate. And ıt may can be possıble for the US, cause US is a county that can provide its own capital alone with it s stronger private sector and important role in the world economy. Actually I don't know exactly what they suggest but thats what ı have understood.
I am not comparing the two. I am saying that your assumption that austerity in downturns is okay for recovery is potentially wrong. Greece's economy isn't doing great right now, just like America's isn't. Cutting huge amounts from the budget would only hurt that, especially for Greece, which can't even control monetary policy.
But, when it comes to Greece, they haven't enaught equity to continue spending and they can't find credit to do this more, maybe with astronomical interest rates, but that's even hard and unsustainable. So, I don't understand that, maybe they suggest the EU to provide enaught resource for Greece's spending and find a solution in that way but that's crazy.
You see the issue with the spending leading to debt, but you are overlooking the revenue aspect. If they cut spending too much, they might hurt revenue, which further worsens the debt problem. They might also hurt expectations, which also worsens the debt problem. The short-term market for government bonds wants stability, the long-term market for government bonds wants spending cuts and sustainability. If you don't provide that short-term stability, you probably can't get to that long-term sustainability.
In the case of Greece though, I personally believe it is game over already. They are sticking with it to save face so the rest don't go down the same road effectively ending the Euro as we know it. The big ones are Spain and Italy in this battle. And the same general issues I described apply.