I think the thread expired some time ago, but since you asked I'll attempt to explain my reasoning on the fine-tuning of the universe. There are a number of physical constants in the universe that if altered slightly would result in a universe unsuitable for life. For example, there's the expansion rate of the universe which is slow enough to allow stars to form, but fast enough to stop gravity from pulling everything back after the big bang. We also have the abundance of carbon in the universe, and somewhere between a handful and scores of others depending on who you ask. The best book I've read on this phenomenon so far is Martin Rees' Just Six Numbers. With the exception of one author, I haven't seen anyone dispute that the universe at least appears to be fine-tuned for the existence of life. Instead the counterarguments focus on alternative explanations for the the fine-tuning.
I think the best counterargument is the multiverse. In fact Rees argues for this explanation in the final chapter of his book. It's important to differentiate here between the multiverse as a scientific and philosophical concept. My problem with the multiverse as a scientific concept is that it's not currently testable, which I think excludes it from the realm of science. That said, just because something isn't testable doesn't mean it is wrong, and God certainly isn't in the realm of science either. So I think both God and the multiverse have to both be approached from a philosophical standpoint. My problem with the multiverse as a philosophical explanation is that we then have to explain where the multiverse came from. This is moving somewhat into the Leibnizian cosmological argument, but God is understood by the monotheistic and some philosophical traditions as a necessary being, which is something that exists eternally and is effectively its own reason for its existence. I have yet to see an author make the case that the multiverse is philosophically necessary. Or to put it differently, the multiverse as a proposed explanation isn't foundational for existence in the way that God is generally conceived to be, and has less explanatory power (in a metaphysical sense).
There are a number of other counterarguments, which I think range from bad to not quite as good as the multiverse. I'd be inclined to address them, if not for the fact that I don't think anyone's reading this thread anymore, and even if they were I'm approaching the TL;DR point.
Keep in mind that when I said I thought this was a strong argument for the existence of God I didn't mean I find it one-hundred percent convincing, but that it is strong relative to the other arguments I've encountered. I think it is at least possible that a multiverse exists and is necessary for reasons we can't comprehend. To clarify, I find the combination of the seven arguments I mentioned above gets me to about a 2.3 on the Dawkin's Scale, but if I only had fine-tuning I think I'd be somewhere around a 4 or 5.