The most likely course of action is that those who object to serving will not be imprisoned, but will be treated like anyone else (e.g. Palestinian citizens of Israel) who doesn’t serve in the army, and that any government support for yeshivos will be tied to military service. If the army also decides to accomodate hareidim in the military (at the very least in special units that are conducted according to halacha), the crisis will pass.
There are many in the zionist movement who believe that they can use conscription to break the hareidi community, and that after three years in a Mitsvah-free atmosphere the conscripts will come back as good secular (or at least “dati”) zionists, but that’s unlikely. Such policies would encourage widespread resistance and probably undermine the state (undermine as in forcing many hareidim to adopt an Eidas hareidus/Satmar/Neturei Karta position, and support a one-state solution based on Palestinian control and Jewish autonomy).. The zionists are sane enough to not push that hard.