I was asked this question the other day, and I found it a bit difficult to answer. I myself have been an atheist since age 15 (20 years sane), and primarily have been a registered Democrat for most of my life.
That said, I wouldn't call myself liberal in the modern sense of the word. Despite the present day polling, I think in a general sense most atheists wouldn't qualify as liberals either. Modern liberalism has a touchy-feely quality not germane to most atheists.
Now liberalism in the traditional sense might better fit the sensibilities of an atheist. Indeed most atheists fit politically into one of three groups. Progressives, Libertarians or Neo-Conservatives.
At the polls, however, when push comes to shove, atheists vote Democrat. Why is that?
Atheism has a profound effect on political positions. On almost any major issue atheists tend to arrive at very different conclusions than their religious counter-parts. Even when their interests seem to align, how they get there is wildly different.
I can't speak for all atheists, but I have noticed some common themes among other atheists I've known. In the most general sense it seems that atheists tend to gravitate to concrete policies rather than idealistic principles.
An example of this would be the desire for universal human rights. There is a moralistic approach to human rights, which is predominant on the left. Atheists tend to be carry the same values, but come upon it in a far more rational sense. To most atheists I know, human rights represent a pragmatic must for a healthy society. The whole 'this is how we should act' notion is almost nonsensical. It is more a matter of what yields the best outcome.
Global warming is another area I see this accidental overlap with some environmentalists. There are many, who believe in a sort natural order which humans should adhere to. Atheists don't tend to see a moral need for conservation, but rather recognize the practical balance between consumption and conservation. Sustainability isn't a moral good. It is just the only rational way to maintain a society.
In these overlaps I think the answer to my question lies. Atheists vote Democrat, because Democrats have taken more pragmatic positions.
I don't think anyone really becomes an atheist. Rather one lets go of all notions they'd like to believe, but just can't rationalize to themselves anymore. It is a moment of brutal honesty, where you say to yourself that you better start dealing with the world the way it actually is. In doing so you let go of many of the should's and should not's, which lack any clear reasons.
For some reason many religious people think that this diminishes the role of humans, but I would disagree. The need for liberty is essential in an atheist's quest. Survival trumps noble sacrifice, so the mechanisms for survival become far more important in an atheist's worldview. Society exists to serve the individuals who make it up.
Republicans don't feel the need to proactively fix problems, because at the heart of their theology, God will figure out whatever we leave undone. There is no such solace in atheism. Either we fix the problem, or we suffer as a result of our own inaction. This is probably why some atheists have chased the neo-conservative remake the world nonsense.
At the same time atheists are cautious of institutional power, which probably explains the libertarian overlaps. The enlightenment philosophies closely related with early atheism reject the dominance of institutional tradition over human experience.
Perhaps this is just another rambling diary, but I really did find the question interesting.