American atheists are less likely to be affiliated to either of the two main political parties. 
This author knows of only one Atheist Political Party, the National Atheist Party in the United States. Atheists hold a wide range of different political opinions and by no means all necessarily agree about politics. Atheists agree only that there is no evidence for the existence of God.
Liberals or Social Democrats
Atheists tend to support Liberal or Social Democrat parties.  Only a minority of atheists are politically conservative because conservatives are traditional. And traditional people tend to support Christianity or some other traditional religion. Political liberals are in favour of helping minorities that face discrimination. Atheists sometimes face discrimination and therefore tend to favor political groups that would protect them. In the United States atheists are far more likely to support the Democratic Party rather than the Republicans, still a substantial minority are Libertarians or Conservatives.  
Liberal minded atheists might argue further that atheists support liberal and social democrat causes because they follow the scientific method and focus on improving conditions in this world (as all political parties claim). In their opinion liberal and social democrat policies are better at improving life here. Liberal minded atheists might also argue that countries like Denmark and the rest of Scandinavia are better than the United States at making their people happy, despite the disadvantages of lower living standards, sparser populations and harsher Northern European climates.
Chris Hallquist a fairly popular atheist blogger has changed from Libertarian to Liberal because he decided that rich and poor people matter equally and the American Democratic Party he believes is better at improving conditions for everyone. 
Libertarian political parties, which are considered very politically conservative by anti-capitalist liberals and social democrats, have a large number,if not majority, of members being atheist. Objectivism, also incorrectly considered very conservative by liberal types due to it's moral support of capitalism and rejection of pacifism, holds that there are no gods, or any other form of mysticism in the universe. Objectivists in the USA are often divided between voting Republican (if doctrinaire) or libertarian (if less doctrinaire). They have sometimes voted for a Democrat if urged to, for purely tactical reasons by Objectivist leaders, to send a message to Republican leaders that they are being too religious and/or in the hopes that a particular Democratic candidate will so badly damage the Democratic Party that it will dissolve. Neither are traditionally socially conservative. Libertarians strongly oppose religion based restrictions on freedom for consenting adults to act in ways that do not harm other people.
An atheist ruler would not feel that he has a God given imperative to pursue certain policies regardless of evidence. Such policies as banning religious advertising or evangelizing would raise free speech issues and could easily be counterproductive.
Telling people they shouldn't, or, god forbid, can't worship who and how they please will quickly push things in the other direction. People love being the Oppressed Righteous.
There may be a case for limiting the money people are allowed to spend on religious or freethought advertising. Any limit would have to cover both to ensure fairness.
Religious indoctrination of children before they are old enough to think critically is an issue for many atheists. Many atheists believe that frightening children about Hell is a form of child abuse and should be illegal.
American atheists are overwhelmingly pro-choice some with reservations, in favor of gay marriage, against school sponsored prayers. 
Atheists in Office
- Atheists note that few politicians have been willing to identify as non-theists, since until recently such revelations would have been "political suicide", and welcomed Democratic California Representative Pete Stark's 2007 decision to come out as the first openly nontheistic member of Congress. In 2009, City Councilman Cecil Bothwell of Asheville, North Carolina was called "unworthy of his seat" because of his open atheism, well Carolina is in the Bible Belt. Indeed, several polls have shown that about 50 percent of Americans would not vote for a well-qualified atheist for president.