It's an important question.
I think the biggest wild card here is awareness of the extent of casualties and whether or not those will actually impact public opinion. At the moment it's difficult to predict, but it is very clear that the number of casualties is being played down on the Putin side.
There has been also some speculation that the use of groups of volunteers, as well as ordinary soldiers from parts of Russia like the Caucasus, is specifically aimed to ensure that casualties are primarily ethnic minorities and that as a result the casualties will not resonate widely through Russian public opinion, which is 80% ethnically Russian—