The questions are two-fold: (1) what could NATO do, and (2) is there the will to do it?
Considering that the US is currently disarming itself at an alarming pace, as are most of the original NATO members, NATO may not in fact be able to do anything, even if the resolve is there; during the attacks on Libya the Europeans ran low on munitions - ran out. A 2011 WaPo article on the subject
put the issue succinctly:
Less than a month into the Libyan conflict, NATO is running short of precision bombs, highlighting the limitations of Britain, France and other European countries in sustaining even a relatively small military action over an extended period of time, according to senior NATO and U.S. officials.
* * *
NATO officials said that their operational tempo has not decreased since the United States relinquished command of the Libya operation and withdrew its strike aircraft at the beginning of April. More planes, they said, would not necessarily result immediately in more strike missions.
But, they said, the current bombing rate by the participating nations is not sustainable. “The reason we need more capability isn’t because we aren’t hitting what we see — it’s so that we can sustain the ability to do so. One problem is flight time, the other is munitions,” said another official, one of several who were not authorized to discuss the issue on the record.
European arsenals of laser-guided bombs, the NATO weapon of choice in the Libyan campaign, have been quickly depleted, officials said. Although the United States has significant stockpiles, its munitions do not fit on the British- and French-made planes that have flown the bulk of the missions.
* * *
If the Europeans couldn't keep up with attacking Libya, then how on Earth would anyone believe they could keep up in a conflict with Russia? To call Libya a 99-pound weakling when compared to Russia is to insult 99-pound weaklings. And the US may not be in a substantially better position either, given Obama's cut-to-the-bones military budgets.
And make no mistake about it, once a hot war starts with Russia, Russia will not be content to sit on its laurels just because the Europeans have run out of bombs; no, Putin will take the opportunity to sweep into Europe and start adding brand new pieces of Europe to the traditional Russian empire. Poland has, if I recollect, been building up its military forces, so they might be able to fend off a direct invasion by Russian forces, but the countries directly south of Poland are not exactly defensive powerhouses and Russia has already started conquering one - Ukraine - so it's quite possible that Russia would choose to sweep down through Ukraine - maybe pick up Belarus - plow through Moldova, south around the Carpathian Mountains, and up toward Austria.
However, despite being short on conventional arms, the Europeans do have nuclear weapons, but I doubt those weapons would be used, at all, until and unless Russia was knocking on the gates of Berlin and Paris - and maybe not even then. Which segues into the second question: does NATO have the will to do anything? My guess is that NATO - i.e., the original European members and the US - would not resort to military force to protect the Baltic states and would only do so if/when Russia started making serious moves on Poland, or as per my wholly speculative, la-la-land thoughts above, started to push through the southern East European states on its way around the Carpathian Mountains. It is only at that point, when it becomes clear that Putin intends to take as much of Europe as he can, that NATO would finally resort to force.
Why would NATO's response be so anemic? Because any hot conflict with Russia would not be some sort of tit-for-tat, step-by-step escalation; once NATO attacks Russian forces, Putin will throw Russia's entire military might against Europe and that is something that none of the Europeans or Obama have the stomache to countenance. So they will, as they did in the 30s with Hitler, hold on to the last shreds of their illusions that, with each conquest, Putin will finally be satiated and stop - until he doesn't. That also means that Russia will have the initiative, because it will already have its forces mobilized and on the move; NATO forces would most likely stay on-base, even if they were on alert, until it finally becomes impossible for NATO to deny that Putin intends to invade Western Europe.
And here comes the most unsettling thought: I'm confident NATO wouldn't use nukes first, but I am not so sure at what point Putin would be willing to use Russia's nukes. He won't use them when he's on the offensive - why irradiate the ground you're about to occupy? - but he may very well be willing to use them as a last ditch defensive weapon if NATO were able to push back on a hypothetical Russian invasion of the rest of Europe. Even if NATO makes it clear that it will stop once it gets to the Russian border, that may not be sufficient to prevent Putin's use of nukes. If it appears that his vision of a new Russian empire is a lost cause, then he might very well lash out at Europe - maybe even the US, although I think that less likely - on the basis that "if I can't have it, then neither can you."