Governors would appoint temporary senators and schedule special house elections. A worse scenario is where a very small number remain alive. While the self imposed rules define how large a quorum must be, there is no constitutional rule. This would be an interesting supreme court challenge to see if 3 hypothetical surviving house members could change the house quorum rules and then pass bills as a 3 person body.
They would still need the Senate (what's left of it + the quickest appointments) and the president. The president would likely take on emergency powers to deal with what would obviously be a major crisis. After some rushed special elections, Congress could get back to work and remove whatever emergency powers were given to the president. It would take many years to really bring politics back to normal though.
