I just left the following comment at an old haunt of mine:
If something occurs that is outside of not only my own personal experience, but the cumulative experience of science, especially since science exists to test boundaries and conditions to see what the laws of nature are and when/if they change, much skepticism should be brought to bear on the claim.
I would say it is a good deal simpler than you are making it here, and perhaps this could be seen more clearly if we remove the context from "miracle" to "violation" of the laws of nature. Suppose that I, scientist X, am working under conditions that no one has worked under before: say, a particle accelerator of potential 20 TeV. If I see something under those conditions that "appears" to violate the laws of physics, the same amount of scrutiny should be brought to bear on my claim as any other claim that a violation has occurred, be it of divine origin or not. And the purpose of the doubt here is to actually find out the truth: the verification principle in the philosophy of science. If the claim is true, and if the violation is natural, then the conditions and test may be repeated and ought to produce the same "violation": at which time, and once fully described, it no longer is a violation, but another law of nature!
On the other hand, suppose that we aren't discovering new laws of nature by creating conditions and tests which are extraordinary, but rather we're in the realm of the mundane. In these conditions, a supposed violation would probably draw just as much scrutiny from you (a believer) as from me (an unbeliever). If I claim that I have a dragon in my shed (to use Sagan as you did in your post), for instance, you would be naturally skeptical and would require more evidence than my "say-so" about it. But if I claim to have a lawn mower in my shed, you won't even blink.
Ditto with religion: the issue is not whether or not a God logically could violate the laws of nature, but whether the evidence we have (the say-so of anonymous persons 2000 years ago) is enough to convince us that violations did happen.