Russia is not a Western country, but the Russians are as educated and sophisticated as a Western population, perhaps more so. Rather than trusting the establishment media, millions have been turning to the internet, or talking on the phone with friends or relatives in Ukraine, to get information from a broader range of sources. The fact that the target is Ukraine matters a lot too. Despite the ghastly history dividing them, Russia and Ukraine have common roots and are very culturally similar, probably more so even than the US and Canada are. War against close relatives is a tough sell.
This raises a real question of how much Putin could rely on the Russian army if he chooses to widen the war. The army is drawn from the people and has broadly the same attitudes. Soldiers are trained to obey orders, but in this case, they'd be obeying reluctantly at best.
This brings me to an odd point about the Crimea invasion -- this is a war in which nobody has died yet. Crimea is about as big as Massachusetts, with two million people, and Russia has invaded and occupied it with a force now estimated at 16,000 men -- so this is a fairly large-scale military operation, yet there have been no casualties. That can only mean that leaders on both sides have given a high priority to avoiding actual combat.
The Russians have given several ultimatums to surrounded Ukrainian troops and ships in Crimea to surrender, then done nothing when the deadlines passed. In an especially striking incident yesterday, a column of Ukrainian troops left their base and marched unarmed toward a nearby Russian-held airstrip, ignoring Russian orders to stop. The confrontation ended with warning shots fired -- but again, no actual fighting.
This seems to be a war that nobody really wants to fight. Russian troops engaged in "military exercises" near the Ukrainian border have already been pulled back to their bases. Putin now knows he has no support from his own people for what he's doing. Things could still go terribly wrong, but the chances of a good outcome look much better than they did when the invasion began.