Palin is not a House member, and even though nothing says the Speaker has to be a member of the House of Representatives there has never been a speaker who was not. And never will be.
Which is more unlikely, choosing a Speaker from outside the House membership, or shutting down Congress because they can’t find anyone within it able to garner 218 votes? If we’re not at the latter now we’re at least closer than we’ve been in a long time. The Conservative minority might even take the shutdown over another RINO speaker.