On June 26, 2002, Bush nominated Griffin to a Michigan seat on the United States Court of Appeals for the Sixth Circuit vacated by Damon Keith, who assumed senior status in 1995.

Previously, on November 8, 2001, President Bush had nominated Henry Saad, David McKeague and Susan Bieke Neilson to three other Michigan seats on the Sixth Circuit.

In its assessment of his nomination, the Independent Judiciary project of the liberal group Alliance for Justice described Griffin as a "deeply conservative jurist".

In March 2003, Michigan's two Democratic senators, Carl Levin (who defeated Griffin's father, Robert P. Griffin, in his bid for re-election in 1978) and Debbie Stabenow announced that they would blue-slip all Bush judicial nominees from Michigan because Bush refused to renominate Helene White and Kathleen McCree Lewis, two Michigan nominees to the Sixth Circuit whose nominations the Senate Republicans had refused to process during President Bill Clinton's second term.

In order to defuse the volatile situation, fourteen moderate Republican and Democratic senators called the Gang of 14 joined together to forge an agreement to guarantee certain filibustered nominations up or down votes.