It's not clear whether ID advocates are specifically arguing for an influence that is supernatural or merely sentient. It should be made clear, however, that any attempt to claim supernatural influence as an explanation is logically inconsistent – a fake explanation.
To claim that a given phenomenon involves the supernatural is to be claiming that it not only operates by laws we do not currently understand, but by laws that we will never come to understand merely by studying the phenomenon. This is quite a claim to make without huge amounts of evidence that the laws of nature we currently understand are being violated – and even in that case, history has shown repeatedly that we do eventually come to understand seemingly inexplicable phenomena once we have identified them.
In order to make a serious case for the supernatural, one would have to (1) show clearly a phenomenon which was not explained by our present science, (2) wait many years for repeated failures to make any headway whatsoever in studying it.