This Wall Street Journal article on the pope makes all kinds of broad claims about his political power without actually providing any evidence. Annoyingly, it also has to bring up Hugo Chávez, claiming that his death opened a political void into which the pope can step--"the Latin America left has no leader" message is unfortunately pervasive in the media. Evidence for papal power includes:
Weeks into his papacy, the pontiff sought to calm tensions in Venezuela after a contested election to replace Mr. Chávez in April started devolving into deadly protests. He issued a statement calling for dialogue.
Giving a statement calling for dialogue does not amount to being a major political player. I don't think anything Pope Francis has done has demonstrated any real political power, if by that we mean truly influencing the course of events and/or prompting political leaders to pursue particular policies.
I am not saying the pope will not have any political sway--though I tend to think it will be limited--but rather we don't yet have much evidence for it. If he does have sway, though, I think the article misses another point. He won't influence leftist presidents who already agree and focus on poverty, but rather will likely be used by those presidents to justify greater social spending. In other words, he won't really be the source of change, but rather will serve as a rationale for change.