Pope Francis is actually the fourth Pope to visit the US, and all have met at least one President. Pope Benedict XVI met George W Bush in 2008, Pope John Paul II met three Presidents (Carter, Reagan and Clinton), and Pope Paul VI met with Lyndon Johnson in 1965.

All four have addressed the UN during their visits as well.

As far as influencing American politics goes, Reagan and John Paul II reportedly had "private" conversations about dissolving Soviet communism via Poland, the Pope's home country. That they had both been assassination targets in 1981 brought them closer together as well. It may be going too far to say that JPII influenced US politics, since Reagan was already attempting to end the Soviet Union, but his support certainly didn't hurt any.