In 2004 NATO and Ukraine were in very close negotiations over eventual membership. Then Russian Energy Coercion started. Russia has made it quite clear that it does not want a NATO member on their borders.
The Dead Hand of Russian Imperialism is all over this one; The EU relies very heavily on Ukrainian grain (as does Russia) indeed, much of their agrarian agriculture is Western owned. Being even closer to Europe is seen as a threat to Russia and in Moscow NATO and EU are regarded as synonymous.
So, what does the West do regarding the riots? Unless these develop into a widespread civil war, there is no direct role for the EU or NATO; however, if the Ukrainian army decides to defect to the protestors or refuses to support the Government, there is the possibility of Russian 'peacekeeping' intervention. Read: occupation. What does the West do then?
If a civil war does develop - and rioting has spread to other population centres - perhaps an EU sponsored Observer Mission could be proposed, backed up by the promise of PKO forces if conditions continue to deteriorate. Think Kosovo, June 1999. Imagine how different Balkans politics would be now if the Russian intervention at Pristina Airport had not be blocked, using, it seems, James Blunt and his squadron?