It is sometimes used to "prove" that atheists don't exist. Anyone who claims to be an atheist is in denial of the God which they "know" to exist; therefore, they are merely angry at or rebelling against God.
Some modern apologists such as Alvin Plantinga make a more moderate claim, which is that everyone has a sensus divinitatis, but that sin interferes with this sense. In order to restore this sense, one has to request God's help to fix it, presumably through conversion or worship or repentance or supplication. On this view, you can be an atheist by not using this natural sense, but only in the same sense as a person can be functionally blind by never opening her eyes.
Contradicted by scripture
Even the Bible contradicts the simplest view, that everyone knows about God deep down. Psalms 14:1 says, "The fool hath said in his heart, There is no God." It seems hard to argue that anyone could say "in his heart" that there is no God while not believing that there is no God. Therefore, the Bible acknowledges that at least some atheists exist (and they are "fools" by Biblical definition).
Competing views that can't be decided upon
People have disagreed on the details of the sense itself, whether it is blocked by sin or available to all people, what triggers experiences of God, whether it gives one a mere experience of God or more useful details... Even William Lane Craig, who uses some of the same arguments generally as Plantinga does, has been hesitant to endorse the idea of an innate "sense", and prefers the idea that there is instead an externally controlled "experience" that the believer has in encountering God. An obvious problem here is that it's not possible to objectively settle this question, especially when Christians who in theory believe similar things, find that they can't agree on the nature of the experience that they supposedly share. The problem gets worse when a similar idea inevitably arises within Muslim apologetics.
If the "sense" really is just a type of personal experience, then we're really talking about Argument from personal experience, which has its own problems.
Unverifiable and unfalsifiable
If someone lacks a particular sense, such as if she is blind, she can always figure out that other people can see, and not merely because they can tell her. They would be able to sense certain things at a distance, in a way that she would not be able to sense, and she could infer the existence of sight without just taking anyone's word for it.
But the sensus divinitatis only provides people with a subjective conviction, not information about the world that can be objectively evaluated. So, from the perspective of someone without such a functioning sense, there's no reason to believe that anyone else has such a sense either. That is, no one has a way of showing that they actually have a way to sense God that is actually accurate, and not merely a form of delusion or mistake.