Oregon
Despite its name, this scenario's Oregon is basically Idaho + the Western portion of Oregon and Washington. That's a little confusing, but I though it would be a shame to keep a name as meaningless as "Idaho" while losing the historically significant "Oregon". And considering that this State covers most of the land that used to be America's portion of Oregon Country, I think the name is pretty fitting. Anyway, Oregon would be a large - not as large as Lincoln, but still - sparsely populated and rural State. Under this arrangement, rural conservatives living east of the Cascade Range would finally be free from the political alienation they suffer IRL in the liberal-leaning OR and WA. Actually, they might even feel that their new State is a bit too conservative for their tastes.
OR Presidential election results, 1960-2012:
On Dave's maps, Oregon would always be a deep-blue State. Republican Presidential candidates perform even better there than in neighboring Lincoln, regularly winning over 60% of the vote. This was one of LBJ's weakest States, giving him less than 55% (a performance comparable to Utah's). And apart from him, no Democrat has ever come close to carrying the State's 6 or 7 Electoral Votes. Since 1968, and excluding election where Perot spoiled a large number of Republican votes, Republicans have always won an absolute majority and distanced their Democratic opponents by at least 15 points. Clearly, Idaho's influence would be significant, although in a "lighter and softer" version. Oregon wouldn't be the Republican fortress that Idaho is: in 2012 for example, Romney "only" won it by 23 points, instead of 32 in IRL Idaho. The areas in the Western part of the State would have a significant moderating influence and make the State's politics less lopsided. Nonetheless, Democrats would have a very hard time winning any statewide election in the modern era.
Capital: It would be possible to keep Boise, although it becomes a little southern for the State's new demographic center. Spokane could be an alternative, though it has the opposite problem.
Governor: Butch Otter - oddly enough, I can't find anyone else with a gubernatorial profile.
Senators: Greg Walden (class 2) and Cathy McMorris Rodgers (class 3) - guess I evened things out by axing both Idaho Senators. 
Representatives: It would be pretty interesting to see how the districts would be drawn if they could cross the ID/OR/WA border. But barring an upset, the most likely result is still 5R-0D.
This is my favorite TL on this forum, bar none. A question on your Senators here - would Hood River (where Greg Walden lives) be in Oregon or Washington in this scenario? It's not far from Portland, all things. Eastern Oregon is so very underpopulated compared to WA that Bend is really the only population center on that side of the mountains, but Hood River is more in the mountains than across them.
The interesting political case you'd likely see in a state like this is alienation from North-South, a true Boise-Spokane rivalry with the conservative, heavily-Mormon Boise region pitted against the more moderate Spokane area. Coeur d'Alene would probably be considered part of a larger Spokane metro in this situation, too.
