I actually think wait times will triple or more, at certain libraries. Especially popular ones like FLP.
But I think it will be a short-term issue. FLP can probably afford to buy more licenses and they presumably will do so. Heavy-users (like myself) will adapt -- heavy-users are rarely using the library for new books, and we usually have a big enough To-Read list that a longer wait at the library isn't a major issue. (I'm "30 of 30" on several books right now alone. Meh.) Light-users, including the new Amazon users, will probably become annoyed and then stop using the system, which will bring wait times back to a more stable spot.
As for Amazon being blamed: Meh. Some people will gripe online about the wait times. Some Amazon users will gripe that they weren't missing anything with libraries because "nothing is ever available". A LOT of people will defend the Kindlers' right to the libraries despite most people not arguing against that point. (See also, kitten juggling.) Mobile Reads moderators will have to issue gentle warnings against personal attacks. Life will continue as usual.