If Cheney dies, does Bush have to name a new veep,

Sure, under normal circumstances such a coronation would be a big advantage. This is the first election since Eisenhower-Stevenson that hasn’t seen an incumbent president or vice-president as the candidate of one of the parties.

The only trouble is that Bush’s popularity is so low that people are arguing over whether he’s the most unpopular president in history, or only the second most unpopular. And over whether he’s the most incompetent president of the modern era, or the most incompetent president of all time. Bush’s endorsement isn’t exactly a feather in your cap.

[QUOTE=DSYoungEsq
The more cogent point is that, without a time limit, unless someone with “standing” to bring suit does so, no mechanism exists for the courts to force the President to name someone. Presumably, this would be handled through public political pressure.[/QUOTE]

Are you considering what effect ‘political pressure’ had on Bush to replace Gonzales? Sure, it eventually worked, on Gonzales, but I don’t think Bush was anywhere near backing down until Gonzales blinked.
Bush has repeatedly ignored political pressure, even from his own party and his own advisors.

I’m not saying what would happen at all. I’m simply saying that there wouldn’t be a lawsuit because no one would have standing to bring one. Possibly.