That is not what Sumner says, of course. He says that the Fed can just announce a target for nominal GDP, and the markets will obey.
I find that highly implausible for nominal GDP, but I do find it plausible for the exchange rate. If the Fed announced a policy of "20 percent weaker dollar or bust," and proceeded to buy euros, yen, and other currencies, by golly, I do not think that private speculators would try to get in the way. And if foreign governments tried to get in the way, that would probably lead to some sort of worldwide monetary expansion that I imagine would make Sumner happy.
One point to make here is that this represents another reason to reject the notion of a liquidity trap. If the Fed runs out of T-bills to buy, it can always buy foreign currencies.
However, I cannot leave this issue without referring to the two-regime theory of monetary policy, which would say that this sort of policy risks moving the U.S. into a regime where the inflation rate becomes high and variable. Instead of keeping cash in mattresses, people will try to conserve on cash, and this will raise the velocity of money, even as the Fed is expanding the money supply. There is a risk that we will overshoot the inflation target. If higher inflation solves a lot of our unemployment problem, then, fine, Scott Sumner is a hero. If not, then, well, he is something else.
But it is certainly amusing to see Sumner dismiss a policy option as "too controversial," as if it competes with all sorts of noncontroversial alternatives that are in play.
Why is it "too controversial?" Is it too simple? The status-preservation theory of the Fed is that it wants to maintain an air of mystery and complexity around monetary policy. Buying foreign currency fails to satisfy that.