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By working to elect Democrats everywhere and to elect as many as possible instead of just calculating to win enough to get you a majority through areas you think are "winnable" you eventually get to a point where you have a supermajority and more. Once you have enough Democrats that you don't have to worry about your narrow advantage you can start to work on making the party more liberal again by engaging in serious primary battles without worrying about giving Congress back to the Republicans.
It will be much easier to get rid of the appeasers once these conditions are true.