I trace it back to the first government shutdown, which I think was 95. Republicans turned all pussy after that.
The shutdown certainly resulted in Gingrich resigning and Dennis Hastert emerging. Gingrich was double-crossed by Bill Clinton during negotiations, when Gingrich agreed to terms with Clinton and then Clinton went to the Rose Garden, blamed Gingrich, and took sole credit for restarting the government. Democrats then retaliated against Gingrich with series of trumped up ethics charges. To them, this was ironic payback over Gingrich ousting former Democrat Speaker Jim Wright over ethics charges regarding bulk sales of a campaign pamphlet "book."
Coincidentally, it was John Boehner who led the group of House Republicans who went to Gingrich with the ultimatum to step down.
However, impeachment came after that, so there was still some fight in Republicans in the late 1990s.
-PJ