Not only do we care but we are contractually and honor bound to do it.
If the US didn't come then we would be in breach of our agreements.
Dude, really? I thought you were smarter than that. France was "contractually and honor bound" to start a full scale assault on Germany 15 days after Germany attacked Poland. Instead they made a halfhearted attempt, didn't even finish that, watched Poland get crushed, then did nothing for seven months while waiting for the Germans to attack. And Germany didn't have the ability to destroy every major French city inside of an hour.
If you think the American body politic would rush headlong into war against a country with 8,000 nuclear weapons over the Baltic States I've got a bridge to sell you. We might honor our treaty obligations, but there would be much dithering involved, consultations with the other NATO countries, resolutions at the Security Council, and so on. It's an open question as to whether or not the nations of Western Europe would honor their commitments and without them what does the US do? Glass Moscow? Because that's about the only recourse we'd have; we can't stage the US Army into the theater without cooperation from local allies.
NATO expansion has so diluted the organization that it's hard to take seriously. The lion's share of members can't take care of themselves, never mind contribute to collective defense. There are only FOUR members (out of 28!) that meet their obligation to spend >=2% of GDP on defense. Most every country in Europe continues to cut defense spending even as Russia dismembers one of their neighbors. Would you take NATO seriously if you sat in the Kremlin? I sure as hell wouldn't.
NATO's mission was once summarized as "to keep the Russians out, the Americans in, and the Germans down." Guess what? The Russians are in, the Americans are disinterested, and the Germans have taken over the continent without firing a shot.