Via Peter Suber, Dorothea Salo and Heather Morrison, I see that the AAP/PSP has responded to the new NIH mandate in typical, PRISM-esque fashion. For anything I might have said in response, and much more, read the linked entries -- especially Peter Suber's. I have something else in mind.

The PSP lists its members here ; it didn't take long to compare that list with the list of publishers indexed by SHERPA/RoMEO. Of the 355 publishers in the RoMEO database, 46 are members of PSP; of these, 16 are listed as "grey" (won't allow archiving), 23 are "green" (allow refereed postprint archiving -- NIH mandate compliant) and 7 "pale green" (allow preprint archiving; many "pale green" publishers actually allow postprint archiving and are NIH compliant, but are not listed as green because of various restrictions).

It's not possible to do what I wanted here -- which was to answer the title question. The problem is that the PSP lists 102 about 100 members that aren't indexed by RoMEO. I found that somewhat surprising, particularly since the list includes names I'd have expected to find in RoMEO: FASEB, Stanford U Press, Yale U Press, Cold Spring Harbor Lab Press, NEJM, Highwire Press and others.

Nonetheless, we can say that if the RoMEO-indexed sample (46 of 148, 31%) is representative, then at least 50% of PSP members are already complying with the NIH mandate, and a further 15% at least allow preprint archiving and may even be NIH-compliant.

It's even more unbalanced if we compare the numbers of journals published by each company. Those 46 publishers account for 5901 journals; the grey publishers put out 222 (4%), the green publishers 4243 (72%) and the pale green publishers 1436 (24%).

If the PSP were honest and interested in fairly representing its members, I'd think they would find out (and make public) whether the remaining, non-RoMEO indexed members follow the same pattern. I won't hold my breath.

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Full disclosure: the numbers above are not 100% accurate, since the comparison between the two lists was not always straightforward. For instance, RoMEO indexes "Yale Law School" and the PSP lists "Yale University Press" as a member. I tried to err on the side of the PSP -- for instance, Yale Law is grey, so I included them. There were a few such problematic instances; I very much doubt that they made any difference to the data expressed as percentages, I'd welcome correction and a better dataset, and if anybody wants the Excel files I used I'll be happy to provide them.
Update: see strikethroughs above; some of the overlap issues can be resolved by searching more carefully -- for instance, NEJM is published by Massachusetts Medical Society, which is in RoMEO, and I have no idea how I missed FASEB the first time around. But again, little or no change to the percentages.