Well, more specifically, they were hoping that Ukraine would simply beat the rebels. Until earlier today, that looked likely.
However we now have a major push, reportedly involving a few thousand Russian troops, in the south of the country in Novoazovsk, near the sea of Azov. That isn't well connected to the areas where the rebels were strongest, but it is an area that would provide a handy land bridge to the Crimea.
Putin accurately perceives that the leadership of the west does not have the will to do anything more than maintain the current level of sanctions AND that with relentless and increasing military engagement he can costlessly breakup and seize a good part of the Ukraine.
Not sure that is really accurate. The US and Britain don't really have the will to do anything, largely because of their extensive economic interests in Russia, but Germany, Sweden, and most of the Eastern European countries are very anxious about any kind of Russian invasion of disputed areas in eastern Europe, for obvious reasons. The Berlin wall came down in living memory.
The best response is still economic. Russia is militarily stronger than NATO in this region. Russia will unite behind Putin if faced with an existential threat, like a militarisation of the border, but economic measures threaten both the oligarchary and the ordinary people. I agree that beefing up defences in the Baltic and in Ukraine itself is necessary, but accompanying this with grandstanding military threats is counter-productive. Keep the talk about political and economic measures, and make sure Russia can't attack the Baltic without attacking (probably small numbers) of western troops on the ground.