New on the U.S. Supreme Court docket is application 09A1121, Rod R. Blagojevich and Robert Blagojevich, Applicants v. United States. The entries to date:
May 18 2010 Application (09A1121) for a stay of trial proceedings, submitted to Justice Stevens.
May 21 2010 Response requested - Due May 28, 2010.
So Justice Stevens did not dismiss this application immediately, nor has he yet referred it to the full court. I expect he will refer it, though, if it appears to have any merit after receiving the response. He is most unlikely to actually grant the stay on his own.