The Baltics are a lost cause, but without an alternative focus of authority (Yeltsin), the rest of the Soviet state would totter on. Even in OTL, most people did actually keep their heads down in what was really a struggle between the elites.I can't see there being succesful coup. There was too much of opposition for such thing. Even if coupers kill Gorbachev and Yeltisn, this probably would lead to collapse of Soviet state or even civil war.
This is Russia. Public support never matters.Civil war is likely. The coup hadnt much public support. But that doesnt mean they dont choose to fight it out.....if they can get some early wins.