If Judge Alito (a conservative) replaces Justice O'Connor (a moderate conservative), that probably would shift the court in some measure to the right. When Justice Ginsburg (a moderate liberal) replaced Justice White (a mixed bag, moderately liberal on some things, centrist on some, conservative on most culture war issues, including abortion, the Establishment Clause, and gay rights), that shifted the court in some measure to the left. But, according to David Boaz, writing in Reason:

In the past three months, the major media have repeatedly hammered away at the theme that Judge Samuel Alito Jr. would "shift the Supreme Court to the right" if he replaced retiring Justice Sandra Day O'Connor.

According to Lexis/Nexis, major newspapers have used the phrase "shift the court" 36 times in their Alito coverage. They have referred to the "balance of the court" 32 times and "the court's balance" another 15. "Shift to the right" accounted for another 18 mentions.

Major radio and television programs indexed by Lexis/Nexis have used those phrases 63 times. CNN told viewers that Alito would "tilt the balance of the court" twice on the day President Bush nominated him. NPR's first-day story on "Morning Edition" was headlined "Alito could move court dramatically to the right." ...

[But around the time of the Ginsburg appointment, n]ot a single major newspaper used the phrases "shift the court," "shift to the left," or "balance of the court" in the six weeks between Clinton's nomination and the Senate's ratification of Ginsburg. Only one story in the Cleveland Plain-Dealer mentioned the "court's balance," and that writer thought that Ginsburg would move a "far right" court "toward the center."

The only network broadcast to use any of those phrases was an NPR interview in which liberal law professor Paul Rothstein of Georgetown University said that Ginsburg might offer a "subtle change ... a nuance" in "the balance of the court" because she would line up with Justice O'Connor in the center....