The pro-russians in the east have moved in mass to Donbas and even then, you really have no way of proving one way or another how hard they will resist or for how long. In general, the population in the east's opinion matters little, as this is an all-out military war between states and those areas will be swiftly taken by Russia anyway.
It's possible that if Russia drives to the Dneiper both the U.S. and NATO will intervene militarily and with Ukrainian permission flood western Ukraine with troops and then proceed to attempt to mediate the conflict.
If that happens after peace is maintained Russia could very well experience a 'troubles' or Vietnam style situation were the rump Ukraine which would then be under NATO protection could then funnel in random arms in and supply rebel/terrorist cells with arms causing headaches down the road.