Why do many, if not most contemporary philosophers (especially naturalist analytical ones à la Quine) believe in the existence of a set of unchanging natural laws despite the fact that this assertion has not, and probably cannot, be substantiated? By 'natural laws,' I mean laws like those associated with physics, etc. rather than laws dictating which sorts of inferential deductions are valid/invalid. Would this belief fare better when faced with a Russell's teacup-style argument than theism does?

I'm not sure what, exactly, leads philosophers to believe in "unchanging laws," and I'm also not sure in what sense such laws cannot be substantiated. I'll focus on the latter. If nothing else, can't they be confirmed to some degree? You should expect that a world without any unchanging laws would look one way (perhaps random, unpredictable, inexplicable stuff happening all the time), while a world with unchanging laws would look another way (exhibiting patterns, being susceptible to some sorts of explanations and predictions, etc.). We seem to be living in a world more like that second, and not so much like the first. So, this seems to confirm, or make more likely, the hypothesis that there is a set of fixed laws governing it all. This argument I just rehearsed is, to be sure, debatable! And one immediately recalls Hume's argument about "induction" or the uniformity of nature. And we do keep finding surprising and (momentarily) inexplicable things (though they do tend to be explained eventually, don't...