Yes, it has a major one.
If we accept the premise of determinism that everything has a cause, then it follows that every cause has a cause. That is, if the cause of my buying a green shirt instead of a yellow shirt is a very complex "equation" that uses biological inputs to return "green shirt", then what was the cause of those biological inputs? My parents genes? And what was the cause of that? And what was the prior preceding cause. And then the cause before that, and the cause before that, ad infinitum.
To continue in Latin, we end up with the reductio ad absurdum conclusion that we can never find the "real" cause because there must always be a prior cause. In other words, if everything has a cause, then nothing has a cause.
But in practice, a determinist will generally stop at a (highly speculative) biological level as the "real" cause. That seems like an arbitrary point in the cause-and-effect process, though. Why not choose an observable point in the process; e.g., the point at which you might say, "I can buy green or yellow -- and though it hardly matters to me, I will choose the green shirt."
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Interestingly this is related to the Cosmological argument for the existence of God, which goes something like this:
If we regress back from effect to cause we must either continue indefinitely or we must arrive at an ultimate cause which is unique in that it has no prior causes - we call this ultimate cause God. Since infinite regression leads to reductio ad absurdum, the alternative must be true - there is a god.
Counter arguments from Hume and Kant et al.
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