John Allen thinks that they might work together well:
Although Benedict’s doctrinal conservatism is certain to create major obstacles in relations with Obama on issues such as abortion, embryonic stem cell research, and gay rights, it might leave other doors open. At the top of the list would be global antipoverty efforts; during a 2007 trip to Brazil, Benedict said that the Catholic Church’s "preferential option for the poor" flows from its faith in Jesus Christ, who was himself poor.
Other areas where Vatican officials perceive at least the possibility of a meeting of minds include disarmament, peacemaking, and environmental protection. They’ve also signaled that Obama might be better positioned to make a difference in two regions of the world where the Vatican has strong interests: the Middle East — including Iraq, where it clashed with George W. Bush over the war — and Africa.
The Dish 