If that split is over something with no middle ground, that every person considers more important than everything else put together (including survival of the democracy), then it quite simply doesn't.
Otherwise, if it's to survive, it does so by compromise, tradeoffs, bargaining, and leaving many people at least a little unhappy but not enough people unhappy enough to dismantle the system.
Otherwise, if it's to survive, it does so by compromise, tradeoffs, bargaining, and leaving many people at least a little unhappy but not enough people unhappy enough to dismantle the system.