How does a primary without Christie or Bush proceed?

[SteveRogers]

Perry gains momentum for a time, and the establishment flirts with backing him, but inevitably another embarrassing gaffe causes him to fall flat.

The party searches for a white night late entrant (a la Fred Thompson in 2008, Perry in 2012). Huckabee et. al.  do some "reconsidering" but ultimately decide not to run. Quite possibly this results in a governor not currently receiving widespread attention being dragged into the race, but a lack of preparation or any real base means they will never live up to the expectations.

All in all, good news for Marco Rubio who probably enters into a protracted battle against Walker for the nomination. But Paul might become a legitimate contender as well.

[SteveRogers]

The same way if Christie and/or Bush do run: Walker wins the nomination.

Does the Tea Party then claim Walker wasn't a real conservative after his subesquent loss?

Oh most definitely.