I don't know whether a survey of the empirical evidence would demonstrate the number of appellate court cases has increased relative to the number of cases the Supreme Court hears, though my observation matches Joe's. Yet I do not see that trend--if there is one--as posing a problem to the stability of the system. The courts of appeals are certainly aware of decisions of other circuits (the parties make sure of that) and the courts are, as a general matter, hesitant to create a circuit split unless the reasoning of another circuit is really flawed. To the extent that circuits disagree, the Supreme Court can step in to resolve the controversy after the courts have had a chance to work it out themselves. I think the system is sufficiently dynamic to respond to the increased reliance upon courts of appeals. In my view the existing structure could only be characterized as broken if people believed the courts of appeals were unable to handle the added burden, but in my view they are doing just fine.
My two cents.