Not at all an expert, but I'm beginning to think that the last papacy set the church on course towards a post-political identity, grounded in liturgical doctrine and charity. Francis was a great pope, but he didn't use the office to press for major changes in doctrine or practice, or to advance the interests of a certain side in geopolitics. The ground of the church was the church.
One danger might be that the powers that be in the national churches, who are very much invested in the political questions aired in church forums and the NYT, might begin to understand that the papacy is shifting to a different ground, and they might not like that. (The newly chosen successor of Peter was brought to Rome and raised to the highest rank in the College of Cardinals and the curia by Francis, so I would expect things to continue on the same course.) Witness the odd coolness from some on the left given the new fellow's (entirely doctrinally correct and charitable) statements about civil unions and such.
Add to that the as-a-given uneasiness of the other half of the NYT-reading Catholic leadership, the wealthy and socially conservative types.
The question might be whether the office is stronger than the political machinations supporting it. Given the office that we're talking about, I think (again, wiseacring non-expert) it might have a fighting chance.