He can always try. Bush did.
There's a pretty good summary of how EOs are used and abused in Wikipedia, here.
It's a sad indictment of Congress and the courts that there have been just two executive orders overturned by the U.S. courts to date, one issued by Harry S Truman nationalizing the steel mills and another by Bill Clintoon attempting to restrict federal contracting to "good" companies that don't hire strike-breakers.
Not mentioned in the Wikipedia article is that the courts routinely throw out cases brought by members of Congress for lack of standing.
No he can’t as an useurper, Obama has no legal authority at all.
Hopefully the Obamination will be kept in check ...