First, I'm not arguing against the obvious point that money can be tight when rates are low. That's just a misunderstanding of economics to make a claim like that. Often, when someone takes issue with a market monetarist they just accuse you of thinking that. I'm not saying that.
My concern is that
Aside from the fact that it's just frustrating to deal with people who talk like this, it's also not helpful from a scientific perspective. The reason why people focus on the base and on short term rates is that that's what the Fed has fairly good control over. It's one thing to say that different economic conditions call for different rates and base money supplies, and to note the difference between a nominal and real rate. It's another thing entirely to say that rates and the base should be ignored and that we should focus our attention on NGDP as a measure of the policy stance, because the whole scientific question at hand is "how does monetary policy (OMOs that affect the base and short rates and maybe long rates for QE) impact NGDP in a depression?"
I don't normally take a particular Popperian attitude towards science*, but the whole problem here can be summed up as the problem of market monetarism (at least as presented by Scott Sumner) can't really be falsified.
This is not the case with Keynesianism or other theories out there to choose from. The policy goal is very distinct from the policy for Keynesians. You can do some back of the envelop calculations with the output gap, Okun's law, and the multiplier and get a policy proposal, and then you can see whether the goal is achieved or not. Of course there are all kinds of arguments left to have about the multiplier's real value, or about whether Romer and Bernstein did a good or bad job forecasting the output gap. There will still be arguments about all that. But nobody ever said anything like "NGDP level goals were not achieved and thus by definition Keynesian policies were not tried". In other words, we can get policy perscriptions wrong because of imperfect knowledge, but we don't define the policy by the achievement of the goal the way Scott Sumner and many other market monetarists seem to.
Sumner could make a case for a Sumner rule like the Taylor rule, and that can be grounded in NGDP levels just like the Taylor rule is grounded in inflation rates. That would be great. But that's very different from what he's doing.
This is the odd thing about reading Friedman too. I'll leave it to the historians of the Depression to validate Friedman's claim about the Fed stance. But there is something inherently odd about pointing to monetary aggregates as a sign that the Fed wasn't doing something right. It could be that, but it could be that your understanding of what Fed policy should be is wrong because it's not moving the broader aggregates.
*To summarize why I don't really approach things in a Popperian way: I think taxonomical and descriptive science is important and that has trouble with the whole "demarcation" attitude. I also think that adjusting theories to deal with empirical problems until we reach the point that another theory offers the better alternative is a good thing, and yet Popper explicitly calls this non-scientific. Finally, I think in an imperfect world we can make good inferences from a body of corroborations, regardless of whether they are corroborations.