[Schmitt] was staunchly anti-Communist throughout the 1920s and critiqued the parliamentary system of Weimar Germany very harshly.
This jibes with what I've read about Schmitt. I agree with TopQuark that "cowardly" may be too harsh a word for Schmitt.
He advocated invoking the famous 48th article of the Weimar Constitution - a provision allowing the President to declare himself a dictator in order to deal with a domestic crisis (specifically, in Schmitt's fears, a Communist coup d'etat).
Irony of ironies - today Arnulf Baring bemoans that Germany no longer has Article 48!
BTW, here in Frankfurt, where I live, Adorno and his academic collaborator Horkheimer are "Säulenheilige", i.e., revered as cerebral giants by those who fashion themselves "intellectuals". The "dialectical method", which Adorno championed, is a sterile, witless exercise in hair-splitting and not-so-crypto-Marxian exegesis. But immensely popular among the chattering classes.
I was saved from falling into this trap by reading at age 17 the clueless, condescending, anti-sensual putdown by Adorno of jazz music. But I wasn't a conservative yet then, which meant that for many years afterward I remained conflicted, confused and lonely.
Since I went to college in America in the 90s, I've been forced to read more Adorno than I would ever have voluntarily read - but I've never read his essay on jazz. I'm a big jazz fan, and I'd like to hear more about his, presumably stupid, anti-jazz comments.