You are going to lose some cities, no doubt about that, unless you are very lucky, very good on the battlefield, or both.
If you reject the Senate's demand for suicide, war erupts.
If you yield and sacrifice your Faction leader, they demand the same thing of your new Faction leader. ONe of two things will stop this cycle- you tell them to bite it and say no, or you run out of family members, and thus you lose the game.
I usually start building armies and leaving them in Italia around the time my Popularity with the People hits about six or seven. I also leave plenty of room for the other factions to expand away from Italia, to avoid these sorts of buld-ups back home. Then, when war is declared, I sweep up all of Italia, go for Greece, and then they are well and truly screwed. Not me.
You might be able to wipe these guys out, if they are Pre-Marian stacks and you are using Legionaries and Post-Marian. The principes and hastati die like flies before even Early Legionaries.