I just wanted to add that any of the bikes mentioned are not 'just barely' up to the task of a cross-country tour -- they are much more than up to it. They could easily do multiple cross-country tours.

***
There seems to be an idea (that a number of people seem to pick up from somewhere), that you need to go to something much more expensive to get a serious touring bike. These are all serious touring bikes.

John Schubert's reviews of these bikes in Adventure Cyclist might be worth a read. He has reviewed many different touring bikes, including the very expensive ones. He makes it clear that some of these less expensive bikes are absolutely fine.

***
For truly heavy-duty, rough, 20,000-mile tours, some heavier-duty componentry (Phil Wood hubs, for example) might be in order. Then again, there are people who have gone around the world, and put more than 20,000 miles on these same bikes (the under-$1000 bikes from REI, Fuji and Jamis).

***
+1 on the LHT -- it is also a great bike, and more than enough.

***
If you check out the REI bikes, the Safari is worth a test ride. It is often underrated. It's one of the best and most reasonably priced touring bikes out there, especially for rough conditions.