WASHINGTON — Justice Ruth Bader Ginsburg is not known for delivering laugh lines. But she drew chuckles from a group of liberal lawyers not long ago while recalling how Justice Elena Kagan, 52, had suggested during an oral argument before the Supreme Court that people born before 1948 were old.

“Next year I will turn 80, God willing,” Justice Ginsburg said. “ ‘I’m not all that old,’ I told my youngest colleague.”

Justice Ginsburg is the eldest member of a court that includes four justices in their 70s, making it among the oldest courts since the New Deal era. Its decisions during this historic “flood season,” as Justice Ginsburg described the end-of-term rush, are likely to make the panel — and the tenure of some of the justices — a significant issue in the presidential campaign....