He will.
I think that would be an incredibly dumb idea. Why? Because from a scheduling standpoint, it would almost have to be a single visit, requiring all of the invitees to coordinate their schedules with that of President Bush. And then we run into the problem of whom to invite. Do we just invite the nine trapped miners and their families? What about the rescuers? And which rescuers? No matter how far the list gets extended, SOMEONE is going to feel unjustly overlooked.
The best thing for President Bush to do would be to wait until things settle down in PA, and then pay a visit to the site of the rescue. Nothing fancy, just a quick, low-key session for President Bush to meet those involved in the ordeal and show his gratitude for ordinary Americans rising to the occasion and overcoming adversity in typical ordinary American fashion. I really think it's important for the president to go to the people instead of making the people come to him. Somehow, I think his interest appears more sincere that way, so long as he doesn't hog the limelight like others have done before him.
Please pardon my use of the term "ordinary". I realize that it's practically an insult when applied to the efforts of those involved in the ongoing rescue efforts. But it's getting late and I can't find my thesaurus.