The response should and would be a declaration of war by NATO against the Russians, and starting to ramp up to take them back by force if necessary. At the same time, probably a full on embargo of Russian trade, freezing of their assets, etc. This alone would cripple Russia’s economy and probably send them into a deep depression. NATO would probably start of by flying interdiction missions to stifle Russia resupply and logistics into the Baltic states and air strikes at depots and caches, C&C and concentrations of Russian forces. Next would be a build up, most likely in Poland. The US would probably send whatever we have on hand right now to Poland and start the process of moving a large conventional force over, and my guess is the other NATO countries would be doing the same thing. Perhaps negotiations with the Ukraine to stage troops there or at least be able to use it to open another front or threaten south western Russia and the Crimea so Russia can’t concentrate everything in the Baltic region.
The thing is, the modern Russia military isn’t what it used to be. They don’t have unlimited (seemingly) troops, tanks, planes etc. They actually have a pretty good core of capable units and troops, but it’s really small. The rest is old Soviet crap that is unevenly maintained and a pool of reserves that have pretty indifferent training and less motivation. I’m not even sure if the Russian military COULD seize all 3 Baltic states as the OP posits. If they did they would be pushing their military to it’s max, especially logistically, and the good units would be spread pretty thin…and vulnerable to being destroyed in detail.