Maybe not, but the USA can't defend the entire world. And Yes, Putin sees this as a cake-walk. Ukraine has been independent for 20 years, and they have faced Putin for nearly 15 of them. If they have no sense of trying to maintain their own culture and uniqueness among nations, have had no fear of Russia in that time, and their government has instead spent its time trying to see how much money they can steal, then its really not a nation - and its a fantasy for the USA to think it can be defended.
Well, you've just made a point that most of the Maydan protestors were trying to make: Ukraine has essentially never been out from under Russia's thumb. On the political side, there was fear of Russia by some: In 1992 Prime Minister of Ukraine Leonid Kuchma argued for keeping some of their nukes, but apparently was overruled or arm-twisted otherwise. Later, somewhat more independent President Viktor Yushchenko was poisoned, and most recently, President Viktor Yanukovych proved to be a complete Russian puppet / stooge, erasing any gains that had been made. Ukraine has never been free of heavy-handed Russian interference, but that (and the corruption, not to mention beatings of initially peaceful protesters) is what most of the protesters at the large Maydan demonstrations turned out against.
At present? WE are the ones telling Ukraine not to fight, both by our words, and more strongly, by not giving any meaningful support at all.
The other argument, that the USA can't defend the entire world, is irrelevant. There is no need to. By emphatically defending allies or parties to security agreements now and then, preferably with other allies helping out or contributing financially, the need for such actions is greatly reduced overall. The converse is also true: If we prove worthless as an ally, weak, and untrustworthy, arms escalations and conflicts will break out everywhere. THAT we cannot stop, and it will certainly cause great damage to us. I presently expect, barring a strong President and US resurgence beginning in 2016, a minimum of a mid-level nuclear war by 2050. The one alternative outside of the US that might prevent such is a very rapid climb to global dominance by a Russian / Chinese alliance. I suppose that is a little better outcome than a nuclear war.