It seems interesting to me that the USA has moved steadily right since around the 1960s. The rise of a left-wing religious movement dedicated to social fairness, helping those in need, and a belief that all people deserve help (as opposed to the gospel of wealth where the poor are punished for their alleged sins) would be an interesting variation.
It may have had its best chance in the turbulent Vietnam Era. If instead of the Hippie Movement, prominent religious voices emerge on the political left to demand a more compassionate, more equitable United States, it would undoubtedly change the political situation in the USA.
Religion need not be on the Political Right. In Latin America, the Catholic Church's Liberation Doctrine demands support for social causes. There are, today, well into the tens of millions of Catholics in the United States, many of which hail from Latin America...
If Religion started aligning on the political left in a large way, there would be more social spending, less military spending, and a larger social net for those in need. Government might be somewhat more wasteful, but disasters like the BP oil Spill would probably not happen, so it is hard to say whether this is a better situation or not.
Alternatively, a Right-Wing Overreach is possible as well. If George W. chokes on a pretzel, Dick Cheney becomes President. Cheney is likely to start wars with Iran and potentially North Korea, while having even less regard for personal freedoms. As little as I like W, he was probably the real voice of moderation in his own government.
President Cheney completely discredits the political right. After getting someone like Condoleeza Rice elected in 2004, things go VERY badly for the political right as the USA is left with giant unpopular wars, increasing corporate scandals, and a even more dysfunctional budget. The Political Left is energized like never before, and the Republican Party is left utterly trashed as Rice is defeated by a massive margin in 2008.