I can diagram it perfectly -- or make it read perfectly -- with a few judicious uses/changes of punctuation, and one reordering of words.

Here is the second quote, un-Palinized:

I know that John McCain and I, as his vice president, will do that. Families, we are blessed with that vote of the American people and are elected to serve and are sworn in on January 20. That will be. Our top priority is to defend the American people.

OK this could be fun. Here is my shot at making the Palin sentence readable - by moving words around and replacing "that" with "the".

Our top priority, families, will be to defend the American people. If we are blessed with [the] vote of the American people, are elected to serve and sworn in on January 20, I know that John McCain, and I as his vice president, will do that.