When will the Russian serfs turn on their masters who are sending them off to die?
Without a draft, angst will be limited. That is why Putin doesn't want an all-out war with Ukraine, and his goals there are limited. An all-out war would require a sizable troop commitment, perhaps of hundreds of thousands of troops. Can't get there, while keeping his best troops on the Chinese border, without a draft.
The US was able to gradually pacify Iraq with a relatively small force (~100K men) because Iraq is mostly a no-man’s-land of vast stretches of desert. Ukraine is mostly forest or arable land, with no shortage of places for guerrillas to hide. The US also had a massive technology advantage because of a much larger procurement budget. The Russians will need a much bigger force to pacify all of Ukraine than the US used in Iraq.