It looks as if Ukrainian forces are making slow, measured progress against pro-Russian separatists. If that’s true, this is how I read the rest of the game playing out:
The Ukrainian government wants to re-occupy as much of Ukraine as possible, while at the same time forestalling Russian military action and preserving the hope of a positive economic relationship with Russia. Ukraine also wants a clear message of support from NATO, although it’s not obvious that anyone in Kiev expects that membership will be forthcoming. I suspect that the Ukrainian government is willing to risk some degree of military conflict; a short, sharp defeat at the hands of Russian forces would be painful, but would also help placate Ukrainian nationalists, and would cement the NATO commitment to support (if not defend) Ukraine in the future.
NATO has many partners, and they have a variety of different interests. None want to see war with Russia, however, and few if any would like to see a Russian invasion of Ukraine. Beyond that, NATO’s interests are in preserving an economic and political relationship with Russia, while maximizing Kiev’s control over eastern Ukraine. Tolerance for risk on the latter point varies considerably, but is only in a very few cases (perhaps Poland) as high as in Kiev.
I suspect that NATO will continue to play a supportive role, trying to modify Russia’s behavior with sanctions and the threat of sanctions. It will provide some material and intelligence support for Kiev, while struggling to prevent Ukraine from becoming over-optimistic about the extent of this support.
Putin does not want to invade Ukraine; if he actively sought this end, he would already have ordered military action, rather than allowing the new Ukrainian government to consolidate power and retake some lost territory. He wants two things; to minimize US and European sanctions, and to maximize the size of the buffer zones in the disputed regions. However, Putin has to contend with two other factions. Pro-Russian separatists in Ukraine and Russian nationalists in Russia are both free to seek maximal gains, and can (in tandem) apply pressure to Putin. Putin is hardly invulnerable domestically, and has to take the strength of the nationalists seriously, especially as he’s come to depend on them.
With the separatists apparently no longer holding the upper hand, Russia has two tools; energy, and its military. Energy sanctions are a two way street, as both Europe and Russia lose through a prolonged disruption. The military balance, however, strongly favors Russia; the Russian military is stronger than it was in 2008, and enjoys a more favorable operational position. If Ukrainian government forces push to far, I suspect that the balance will shift and Putin will order much more aggressive military action against Ukraine. This will preserve the buffer zones, placate nationalists, and serve as a warning to the other post-Soviet republics. It will also incur greater sanctions, but if Russia avoids a drive on Kiev these will be manageable.
My guess is that we’ll see a short, conventional war of maneuver between Russia and Ukraine, that the Russian will win, but will restrain its activities to Donetsk, Luhansk, and environs. It’s going to be very difficult for the Ukrainian military to restrain itself short of complete victory over the separatists, and the drive for victory will probably spur Russian intervention. With luck, however, the war will be quick, only moderately destructive, and the political aftermath will be manageable.