If you think majority of Russians living in Ukraine will consider themselves Russian and be happy to be invaded
Er, what even made you believe that I was making an argument along those lines? What I wrote is pretty much the opposite... the separatists were getting crushed precisely because of what you say - that not even most Russian and russophone Ukrainian population in the areas they claim supports it. Russia actually had step up and send in its own troops, and not just weapons and advisors as they did before, to reverse the tide.
The problem is that fighting spirit and dedication are not enough; you still need artillery and tanks and planes to win a war, and people who know how to strategically apply all this. That's where Ukraine is lagging far behind, especially after the significant build-up that Russia had since 2008. And Russian troops are not exactly lacking in motivation, either - they've been fed propaganda about fascists burning people alive and crucifying children, on one hand, and about the "Russian World" on the other hand, and are itching for a fight.
So, regardless of where the sympathies of the majority of Ukrainians lie, if Putin does give the order, Ukraine will fall with no outside help. And I don't know whether it'll get that help. A few months ago I thought that it would be a given, but then we saw basically nothing done over the annexation of Crimea, and very little done over all the affronts since then... and even today Western newspapers are still mulling over maybe more sanctions (?!!).