My understanding is that the more popular saints and prophets did not announce the specifics of their tactically-significant miracles in advance,

In the one referred by MassDriver, where Joshua makes the sun stand still, he does ask for that to happen. Note that many Biblical miracles have the prophets saying what will happen in advance. Most likely the stories never even took place. Similarly, many modern faith healers say what will happen well in advance, but the claimed miracles are simply not impressive.

that more than a few people voted for Bush on the strength of his claim to communicate with God (along with the implication that he can ask for help when needed, and has a better-than-average chance of receiving it)

Do you have a citation for this? Certainly there were people who voted for Bush due to his religion. But I'm not aware of any evidence that a substantial number of people voted for him due to claims that he could talk to God.