Could they actually call together a vote to do so in the very short amount of time before the vote on this bill? The problem is that it is Congress - it would take at least a full day to get them to even agree to call a vote on this at all. And only the group within the GOP that explicitly represents the Tea Party could be counted on to remove Boehner as House speaker.
They, the republicans, don’t need to have a vote per se. They need only poll themselves to see if 221 of their 232 caucus will send a message to Boehner that they have the votes to remove him.