If Mexico signed a military alliance with Russia and accepted to have russian military bases on its soil, what would be the reaction of the US? Of course, Russia is never going to invade a country twice bigger in terms of population than it.

It's a matter of threat management. Even if you know that the guy who's pointing the gun at your head isn't going to fire it, you'd prefer him to stop, or at least throw his gun. Once NATO will have cornered Russia with ultrasonic missiles, then the NATO's ultimatums will have much more power.

I'm against war, and I don't think personally that opting for an aggressive behavior toward our neighbors will wage peace. The US has a very long history of bombing every possible threat on the globe, either economical or military, so I guess your question is quite moot if you think a bit more about it.