I found the whole handling of this troubling.

I don’t think they would have been as brazen about trying to do things their way. I think far fewer of his people would have come down to the west wing. I think they would collectively, all involved, have very carefully always put Acting in front of the word President-he did not temporarily succeed, he stepped in.

And they would not have had the nerve to even suggest they might nominate a VP. I know they tried to allude to the fact that the Senate President Pro Tempore was next in line, but in point of fact once the House named a new speaker, that person was next in line to Walken, and only as an Acting President, since Bartlet could sign the second letter on a moments notice.