<hesitantly places her toe in the boiling water> :)
Interesting points, all.
My answer to the original question would be a definite no, and I think my answer is just a bit different so bear with me a moment. I think the Europeans and Native Americans could NOT coexist because of the blood guilt the European people would have to have embraced. So far as the Native Americans being a 'dirty' people, this simply wasn't true. They practiced better hygiene than an unfortunate number of people I know here in the States :)
No, the problem is they had no defense against the diseases that the Europeans brought along with them. Viruses that had endured centuries of differing evolution and were incredibly deadly to the nearly defenseless Native American population. The greatest murderers of Native Americans was never the settlers, or the Calvary. It was simple flu bugs.
Now, follow my train of logic here. The settlers now were faced with a conundrum. Either accept that your mere presence as uninvited guests on another people's lands has resulted in the deaths of millions of their people or instead take the unfortunately 'human' route and demonize the victim. 'It's not our fault. These people have no concept of proper living. They're savages! Barely better than animals, and usually filthier! No wonder they die in droves!'
This was not done (in most cases, I believe) with foul intent but was simple human nature in justifying their actions by perceiving faults in others. We enslaved black people only after we had talked ourselves into the idea that they were subhuman, without souls (a concept actually taught to black tribes in the early days of expansion into Africa) and we drove the Native Americans before us with the same platitudes ringing in our ears.
In summary - Native Americans and the mainly European settles couldn't live together because WE couldn't own up to it. WE couldn't acknowledge them as equals after those first, completely unintentional atrocities, because we couldn't face ourselves in the mirror again.
Feel free to disagree with me (even violently if you want :) )