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Answer
A "switch in time" (obviously a play on "a stitch in time saves nine") refers to when Justice Roberts did an unexpected change and voted to support one of FDR's new deal pieces of legislation even though he had consistently been against New Deal legislation.
The "saves nine" portion because FDR was threatening a court packing plan to increase the number of justices up to 15 to make sure that the old guard would be outnumbered. (And of course there were and still are nine justices on the Supreme Court)
Answer
"The switch in time that saved nine" refers to US Supreme Court swing voter Justice Owen Roberts' 1937 decision to begin voting with the progressive bloc of justices, ending the Court's blockade of New Deal legislation. This decision is alleged to have been made just in time to prevent Roosevelt from implementing his controversial court-packing scheme. In fact, Congress stripped Roosevelt's provision from the bill and Roberts had apparently decided how he was going to vote on the case prior to Roosevelt announcing his judicial reorganization plan.
Explanation
In April 1937, the Supreme Court's swing voter, Justice Owen Roberts, shifted his vote on New Deal programs from conservative to liberal, giving the Roosevelt administration an important win in West Coast Hotel v. Parrish, (1937), upholding a state minimum wage law. This shift was referred to as "the switch in time that saved nine," meaning Owens' decision to vote with the liberal bloc saved the nine justices from Roosevelt's scheme (the phrase was a play on the old aphorism, "a stitch in time saves nine."). (Historians claim Owens' decision had already been made before the Judiciary Reorganization Bill was announced.) The Court also delivered two unanimous opinions on New Deal-friendly cases the same day. These decisions further decayed voter support for reorganization.
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