Many of the "news analysis" articles showing up in the media about the "dilemmas" facing the Catholic Church suggest what is likely to come if the next Pope is a conservative. Secular criticism of Pope John Paul II was always muted because of his great moral authority from having stood up against the Nazis and then the Communists. And then there was his enormous personal popularity.
The next Pope will not have these advantages. If the next Pope is a conservative, look for an early and ferocious attack on him from the Left. The news media is already preparing the ground for it.
Of course, this will only deepen the red-blue divide in the U.S.