1. Lieberman may back down, perhaps for freedom to vote against repealing the conscription law and of course, patronage. Lapid might also back down, but that’s less likely. Likud might prefer to have Labor as a partner rather than Lieberman or Lapid – in part since Labor’s patronage demands are about the same as Lieberman and Lapid.
2. It might depend on the form that exempting hareidim takes. If, for example, Israel moves towards a volunteer/professional army, with liberal veterans benefits (which are cuurently considered to be unconstitutional discrimination against not veterans), there will be less opposition than to specifically exempting yeshiva students.