CINCINNATI  When he ran for office in 2000, President Bush vowed to appoint “more judges like Clarence Thomas and Antonin Scalia.” On Monday, the opening day of the Supreme Court’s new term, Mr. Bush came to the critical swing state of Ohio to remind Americans that he has lived up to that promise  and to make the case, if only obliquely, that so would Senator John McCain.

“The lesson is clear: Judges matter to every American,” Mr. Bush told members of the Federalist Society, a conservative legal group, after ticking off a list of narrowly decided Supreme Court decisions, including two he regards favorably  one upholding a ban on the medical procedure critics call partial-birth abortion, and another overturning a ban on gun ownership in the District of Columbia.

“Our belief in judicial restraint is shared by the vast majority of the American people,” Mr. Bush said, adding that he had kept his pledge to “seek judges who would faithfully interpret the Constitution  not use the courts to invent laws or dictate social policy.”

Legal experts say Mr. Bush has had a profound impact on the judiciary, reshaping it with a conservative tilt that could long outlast his administration. But with the Supreme Court split 5 to 4 on many decisions, both parties agree that it will take another vacancy  to be filled, presumably, by the next president  to either seal or undo that legacy.