It would be hard. If it collapsed as a party of any national strength, it would remain a party with local regional strength, which would keep it in Congress if not the White House. That is essentially the OTL, until the New Deal charm began to wear off with enough people that the Republicans made ground, almost took the White House in 1948, and retook it in 1952, and took Congress for a short while around one of those years before botching it and having the Democrats retake it.
Even in the 1930's with FDR revered as a God, America was still as far right as Rumsfeldia compared with every other industrialized nation not named Nazi Germany.