Very often when people complain about secular government, they argue that the absence of their god and the absence of an endorsement of their religion is the same as an endorsement of atheism. Does this argument work?

No, absolutely not - it's a ridiculous argument that simply gets passed around and repeated by people who evidently haven't stopped to really think about it. A letter to the editor written by Ken Michel and published in the Fredericksburg Free Lance-Star has a good rebuttal:

When a recipe for chocolate cake calls for only flour, sugar, water and chocolate, do we call this an "atheist" recipe, simply because it does not say "Now add a pinch of God"? No, we do not. Likewise our pledge and motto and currency were not atheist when they did not include God; they were simply neutral regarding faith, not atheistic. It is up to us as individuals to bring the spirit of God to all that we do not up to the government.

Now, strictly speaking I would say that Ken is wrong and that the recipe is, technically, "atheistic" because it is lacking any mention of gods (in the same way that a story could be called "theistic" if gods play a role or are characters). But there is a big difference between lacking any mention of gods and promoting disbelief in gods. A recipe can be atheistic without promoting atheism. A novel can be atheistic without promoting atheism. A law can be atheistic without promoting atheism. The fact that something is atheistic in the very technical sense really isn't important - when was the last time that a Christian or Muslim was troubled by the lack of references to God in a computer manual? It's not something that anyone cares about because they recognize that it's not the same as promoting atheism.

Read More:

• Secularism 101
• Separation of Church and State 101