> Which is only convention, not by law, and in any case, just an arbitrary number
No, its actually set by law, not convention.
> FDR threatened to pack the court with lackeys if they didn't vote in favor of his programs.
FDR proposed legislation to Congress which would have expanded the number of Justices on the Supreme Court. [1] It was not a threat of unilateral action. The President can't appoint people to the Court without an open seat, created by Congress, to appoint them to.
> I suppose, at least, FDR would have had to answer to public opinion if he had actually carried out that threat. Unlike, say, if the secret FISA court were so threatened.
There are two different courts created under FISA (the Foreign Intelligence Surveillance Court and the Foreign Intelligence Surveillance Court of Review), and the members of both are selected by the Chief Justice of the United States from among current members of the federal judiciary.
[1] http://en.wikipedia.org/wiki/Judicial_Procedures_Reform_Bill...