I'm not sure why anyone would promote giving any land to Mexico; that's just crazy. But since you brought up the Mexican-American wars, I was thinking today how this just reinforces something I mentioned earlier.
When the Tejanos and the Texans overthrew the local mexican government, and the Army of Texas captured Santa Anna, they weren't like "Okay, all of Mexico is ours now!!" Why not? because that's ridiculous and stupid, and makes no sense... but that's exactly what happened in Ukraine. We're in charge of all Ukraine now, and if you don't like it, then screw you. But that's not how things work in reality; never has been.
If the Neo-Ukrainian government had negotiated and settled with counter-revolutionaries; I would probably be like "okay, good for them" but instead, they appear to be greedy slimebags that have sucked the entire world into their stupid problems. America has it's own problems- we don't need Ukraine's problems... or Russia's problems... or really even Western Europe's problems, but I suppose after we are done fixing ourselves, we could smack some sense into our European allies... but this Ukraine thing is not our problem. They could have negotiated, and still can negotiate their way out of this.