The main influence of the C J is that he assigns the cases to the various justices to see if they will review them. I can see where this might have some influence. For example, if there is a Second Amendment question on appeal to the Court, it might be referred to Thomas rather than Souter.
Because Roberts was a clerk for Rehnquist and was part of Rehnquist's circle of friends he had mentored, I hope we will not be disappointed in him. Now everyone should pray that Pres. Bush makes an excellent choice for the O'Connor seat, and does it this week.
Not completely true. Chief Justice also gets to pick who writes the rulings which effects the law. Its not just 5-4 we win, its how the ruling is phrased which provides guidance to the lower courts on what the law is and how similar cases are expected to be handled. A minor deal but the CJ also sets the rules for how the court runs. Rennqueist for example said in their meetings that no one justice can talk more than once until all other justices have spoken. Also, if a CJ is a good politician he can have considerable power in shaping the outcome of a vote and even which issues get taken up by the court.
The court makes their own rules, just like the congress, the chief can have as much power as the majority on the court want him to have.
The court can even force judges to resign.