You would have Nancy Pelosi as Speaker by going in that direction....look at her votes as they were...People would have maintained their vote on the second go round...or the more liberal could have voted Pelosi.
Getting another vote would not have elected another Republican...that was so obvious as the votes were taken, that it would be Boehner, OR Pelosi.
I didn’t realize the whole House participated in the second vote. I didn’t bother to look it up, but that even concerned me about the first vote, not realizing only the Republicans could participate.