Statesmenlike, responsible Republicans — that is, what passes for responsible in the dysfunctional, feedback-loop-impaired GOP — seem to have learned exactly two useful lessons from the Newt Gingrich era: Don't shut down the government, and don't impeach the president over nonsense.
OK, it's a little more complicated. The real shutdown lesson seems to be, more or less, not to assume that a government shutdown will magically produce Republican gains, regardless of the context; the other is to avoid impeaching popular presidents when you clearly don't have the votes to convict.
Unfortunately, while House Speaker John Boehner and other marginally responsible Republicans seem to have absorbed that much from Gingrich's disasters, Republicans with less specific memories of the 1990s seem to have taken a different lesson from the Gingrich years: Impeachment and government shutdowns are what "real conservatives" do, and anyone who doesn't support them at the drop of a hat must be either a secret liberal or one of those wimps who are always selling out real conservatives.