Existence is an ontological problem. The problem is simple and phrased as "What is there?" The above and much of this discussion is taken from W. V. Quine's article On What There Is in the book Philosophy of Mathematics: Selected Readings edited by Paul Benacerraf and Hilary Putnam, published by Prentice Hall, copyright 1964.
The answer is likewise simple "Everything exists." This leads to what is everything? The universal quantifier is everything and the existential quantifier is existence. The following mathematical notation ∀X X ∈ ℤ ∃Y Y ∈ ℤ ^ Y = 2X in English means For all integers there exists at least one integer that is two times the original integer.
The issue of existence gets much more complicated when talking of non-existence. When formulating a "difference of opinion" on existence there is a predicament. In particular there is a problem of giving a name to something that does not exist. Giving a name is admittance of existence.
To get back the question "Do unicorns exist?" Well they certainly exist in my mind. Does that mean they exist? Typically we talk of existence in the physical objective world. Quine states at the end of the essay:
From among the various conceptual schemes best suited to these various pursuits, one—the phenomenalistic—claims epistemological priority. Viewed from within the phenomenalistic conceptual scheme, the ontologies of physical objects and mathematical objects are myths. The quality of myth, however, is relative; relative, in this case, to the epistemological point of view. This point of view is one among various, corresponding to one among our various interests and purposes.
To get back to the physical, "Do unicorns exist?" I have only one answer, not to my knowledge. Why? The reason I give this answer is that I do not know all that exists in the physical world. Worse my knowledge as Quine and David Hume say is myth. But as Quine further says the "quality of myth" is relative. So when considering all there is, "Do unicorns exist?" No one knows and if they did that knowledge would be a myth.
I view the existence of God much like the existence of unicorns. I do not have knowledge of God, but lack of that knowledge does not preclude the existence of God. Knowledge of God like knowledge itself is a myth. The quality of the myth is relative to the person.
I must answer the question why is this question important to people concerned with improving the democratic party and helping democrats win elections. Religion is an important part of political discourse. President Bush, the son, used religion to garner votes in his race against Vice President Gore. President Obama also used religion in his race against McCain and even had Rick Warren moderate a debate. For many the question of gay marriage is a religious question. Worse non-Christians and in particular atheists have a difficult time getting elected to office. One wonders when an atheist will be elected president, just like before JFK one could wonder when a Catholic would be elected president.
My point is religion is a part of politics and very much a part of democratic politics and therefore cannot be ignored here. Hence the question of whether or not there is a God will always be a question that will need to be addressed and dealt with.