I'm exploring congressional options in this kind of situation since Obama is fairly useless. I go back to Reagan and think, what would he have done? Well, I'm sure he would have seen this coming (Palin suspected it in 2008) and would have been ready to move military exercises into that region while having ongoing discussions with Putin, making it clear America would not stand by while a free country is invaded by an aggressor like Russia. And, as he did with Granada, not hesitate to go in and fight for Ukraine freedom if they were invaded.
Congressional ability is much less nimble and surgical in their ability to deal with an aggressor nation, but at the same time, it seems that our hands may not have to be completely tied because of Obama's typical Leftist inability to respond decisively.
Rationale could be a few things.
1) America, as the most powerful free country on earth, has been, under the right leadership, a protector of free countries from outside aggression. The freer the world, the safer the world for everyone, including the U.S. (I do NOT advocate the mutton-headed so-called "Bush Doctrine" of invading countries to "make them democratic" (his eventual rationale for invading Iraq after abandoning the WMD rationale - his real reason was to finish the job on Saddam that his dad didn't). The "Bush Doctrine" is repulsive and un-Ameircan. We stand for freedom not invasion and forced servitude.)
2) It also is in America's best interests because other aggressive nations are watching. A strong, decisive response to unwarranted and unwelcomed aggression upon a free nation will make other totalitarian aggressors think twice about their takeover plans. Here, we know China, North Korea, Syria, and Iran are taking notes and making plans accordingly. As a direct result of Obama's hand-wringing indecisiveness, Israel has now had to declare that they will take on Iran without the U.S. who they no longer can rely on.
We cannot play the isolationist game the way we could when Washington was President ("no entangling alliances"). We shouldn't politically or militarily entangle ourselves internationally unnecessarily, but our world has shrunk since the 18th Century and things like the intercontinental nuclear threat makes these things very much a part of U.S. interest.
NOTHING in your rationale justify a US declaration of war to Russia.