How did the Supreme Court begin to change to a more conservative posture?

Answer 1

The Supreme Court became more conservative because many vacancies occurred during Republican administrations, giving conservative Presidents an opportunity to replace liberal justices with more conservative justices. The Court seems to swing from one poll to the other over the course of time.

Both the Roberts Court and the Rehnquist Court have been conservative; prior to that, the Burger Court was moderate and Warren Court was progressive.

The ideology of the US Supreme Court is unlikely to change during President Obama's tenure in office because the two most likely justices to retire (Stevens and Ginsburg) are liberal.