1) First of all, she said: our alliances which we have around the world are dependent on the ability to look out for our friends, and not favor our enemies. end quote.
So yes, Russians are the eternal enemies.
2) Secondly, Putin is the most moderate president. After him, there can be more pro-war presidents, so it can be even worse.
Many Russians are not in favor of this invasion. And many more are coming to feel that way as the "war" becomes an ever greater disaster. They're just too frightened and debilitated to do anything about it. Putin's soon to be replacement will very likely capitalize on this resentment to solidify his/her hold on power once they manage to usurp Putin. He will be blamed for everything (so his supporters can hide from their responsibility) and the new ruler will then set about rebuilding Russian might for the future. Leaving Ukraine to do the same (and to join NATO, most likely).
I have not heard a single American call the Russian people our "enemy". This is not the common sentiment, here. Nor should it be. Nor do I hear anything about Russians calling Americans their "enemy". (Granted, it's hard to hear the other side of the world, but the Youtube interviews I've seen clearly indicate that most Russians are not feeling any great antipathy toward Americans.) Everyone seem to understand that this invasion is all politics, and that it is generally all a very bad idea. Similar to the unfounded and needless U.S. invasion of Iraq.
So whomever you are referring to claiming that Russia is anyone's eternal enemy is full of crap. Putin is the enemy of Ukraine, of the western alliance, and increasingly, of Russia itself. And I predict that he will be removed as a result, sooner or later. Sooner, we all hope. As he deserves to be, and as the war will end immediately after he does.