I am not so sure, the political class, media and elites are very good at ignoring the suffering of other nations when it suits their agenda and their agenda was very much to avoid bad relations or another Cold War with Putin at all costs.
This was the high point in post Cold War Western isolationism and if they press wants to focus on the butchery going on in Syria and the soon to be re-invasion of Iraq by ISIS over Ukraine as they wanted to OTL they would again.
The Western press by in large just wanted to believe and hope Putin would stop acting like a 19th century Imperialist on his own and had the view nothing is worse then another Cold War.
They didn't want to gin up Cold War feelings and they had the final say on how much the public sees and hears about it.
I think you are rather giving this question a stock answer than considering the actual implications of what is suggested in the OP. What I am saying is that the realistic consequences of a significantly bigger Russian campaign in Ukraine would pretty much force much of "the West" out of the "see no evil, hear no evil" stance that has been taken by many IOTL.
IMO, we have dodged several bullets with the situation in Ukraine, simply because the Russian invasion has been so limited, and thus the Ukrainian government and state apparatus has continued to work, if not normally, then at least looking like a fair imitation of normalcy. If the Russian invasion was a lot more extensive, it is very likely that the functioning of the Ukrainian state would be under major risk.
Again, there would be a lot more death, a lot more casualties. This would lead to more need for foreign aid, which would directly affect other European nations. The Ukrainian people and state would be asking and begging for more help, and the international organizations like the Red Cross and the OSCE would confirm that the situation is dire. The Ukrainian state apparatus itself would be in trouble. It was in trouble IOTL, in the days and months after the Maidan, but by and by it managed to rebound quite admirably, all the outside influence, corruption and disruption notwithstanding. After the Maidan, Ukraine managed more or less free and fair parliamentary and presidential elections within a year, making the government legitimate again if it was not strictly that after the events of the Maidan and the aftermath. ITTL, the fact that a lot bigger part of the nation is a battleground would mean that it is much harder for the Ukrainian state to function. The right-wing militias would have more comparative influence, and the central government would be under much more pressure. We would probably see elections postponed indefinitely in 2014, maybe even early 2015. This would sow doubt about the Yatsenuyk government and allow the opening to call it a "Fascist junta" in the Russian fashion. Many more would believe that Kiev is led by extremists who do not want a return to democracy. The situation would breed distrust and instability, and at the end of it we could see Kiev start losing control even in the areas it has managed to control IOTL (discounting those that ITTL would be controlled by Russian soldiers, or would be battlegrounds).
So, by the fall of 2014, ITTL the EU could be looking at a real possibility of a wholesale collapse of the Ukrainian state apparatus and the birth of a Ukraine-sized failed state on its eastern flank. A horrible prospect, one that could mean both a refugee crisis and a massive humanitarian disaster. Simply put, the mere possibility of this would make the European leaders and politicians stand up and take notice. They would be
forced to take measures to support Ukraine and to oppose Russian actions. This would also be demanded by the European press reporting the events in Ukraine. Nobody who was privy to the situation in Europe could be as complacent as people have been IOTL, especially after the crisis of the first months passed and a "new normality" was built in Ukraine.
Like I said above, there is a level (and style) of Russian aggression in Ukraine the European politicians and press have been ready to disregard "not to rock the boat". I believe the Russian government has been counting on just that, and this is also a reason for its attempts to camouflage the events as local opposition and insurgency to create "plausible deniability" and muddy the waters. But there is a line beyond which this process would not work in the same way anymore, and a Russian attempt at much bigger than OTL gains in Ukraine would very likely cross that line. Russia openly waging a large-scale shooting war in Ukraine would mean just that.
Wait what? Outside of Crimea there are no muslims in Ukraine. And the Crimean Tatars aren't the kind that can be easily radicalized.
Our friend mack8 here seems to have bought into the Russian narrative and associated conspiracy theories about Ukraine. The US organizing the Euromaidan pretty much wholesale and the US/NATO directly supporting "CIA death squads", Fascist militias and bands of Jihadists in Ukraine are staples of the Russian narrative. The reference to the "Odessa massacre" (that is the
Trade Unions House fire in Odessa in May 2014) is also a dead giveaway.