Both parties will be fine and will win more elections. They both will find new issuers to fight over and to divide the nation on. There will not be any thrid party come up and take over any other either party, that's a pipe dream.
This.
The Republican Party is not dead. The Democrats were not dead in 1920, the Republicans were not dead in 1936, and there is no way that a party that currently controls the House is dead today. The two-party system will always revive itself. The Republicans will eventually figure out how to avoid alienating youth and minorities as much as they have been.