closer to OTL than you think
I agree that Cheney -- even incumbent Cheney -- gets destroyed no matter what, but I think the predictions of a Lyndon Johnsonesque landslide are a little off. There's simply an entrenched plurality in this country who aren't voting for Obama under any circumstances in 2008.
Here's the math. Obama/Biden lost the following states by enormous margins in OTL:
Alabama (-21.5), Alaska (-21.5), Arkansas (-20), Idaho (-25), Kansas (-15), Kentucky (-16.5), Louisiana (-18.5), Mississippi (-13), Nebraska-AL (-15), Nebraska-3 (-39), Oklahoma (-31), Tennessee (-15), Texas (-12), Utah (-28), West Virginia (-13), and Wyoming (-32). You might be thinking that the Alaska margin reflects some Sarah Palin effect -- and no doubt it does -- but consider that a) Palin was not particularly popular there by the time Nov. 2008 rolled around, b) VP selections rarely have a huge impact even in their home states, and c) Alaska has been an awfully red state for an awfully long time.
This core of states is likely going for the Republican slate in '08 even if the ticket is Zombie Hitler/George Steinbrenner. So that's a baseline of 119 EVs.
With Cheney as the GOP nominee, Obama probably picks up Arizona, Georgia, Missouri, Montana, Nebraska-1, and South Carolina for an extra 48 EVs, making his margin of victory 413-125.
If you really wanted to push the envelope, you could swing 6 more EVs Obama's way from North and South Dakota (each of which Obama lost by ~9 points in OTL -- but consider that these states probably have more regional appeal for Cheney, too). If you think Alaska is in play without Sarah Palin, go ahead and chalk up 3 more to the Democratic ticket. But I don't see how you get any Democrat in 2008 more than 422 EVs.