It seems pretty obvious that if the Indians had not lost millions to disease -- I've seen estimates of 90% of the population wiped out, I'm not sure what the scholarly consensus is, or how reliable any numbers are -- anyway it seems obvious that that would have put them in a much stronger position to resist European colonization. But exactly how would it play out?
At one extreme, one could argue that it would have made little difference. Bear in mind that the reality was not a matter of "Europeans versus Indians". Both groups consisted of many competing nations. When Cortez conquered the Aztecs, a very important factor was that the real situation was not "a tiny band of Spaniards versus a huge empire", but rather, "a tiny band of Spaniards mobilizing many native nations who all had good reason to hate the Incas -- because the Incas regularly tortured, killed and enslaved them -- and leading them against the Incas".
My point being: the actual history was a series of shifting alliances between various European nations and various Indian nations. If there had been more Indians, this would certainly have changed the dynamic, but as for most of history it was some Europeans and some Indians versus other Europeans and other Indians, maybe the Indians would have just killed each other and the end result would have been the same.
At the opposite extreme, one can certainly imagine a scenario where the Indians all banded together to resist the Europeans and throw them off the continent. But that scenario is wildly improbable. It's like saying that Germany could have won World War 2 if only they could have convinced the French and British and Yugoslavians and Greeks to unite with them to fight the invading Americans.
I think there may be some subtle racism here: the idea that of course Britain and France and Germany are distinct nations with distinct history and cultures, but that the Cherokee and the Navajo and Incas are all basically the same, there's really no difference between them, because they're all "just Indians", not "real" nations. Like I've heard many times that Malintzin, the Indian woman who served as a translator and guide to Cortez, was a "traitor to her own people" for helping the Spanish against her fellow Native Americans. Except ... she WAS siding with her own people. Her father had been assassinated by the Aztecs for refusing to submit to their power. Would you really say that she had some moral obligation to help the people who murdered her father, just because they were born on the same continent? That's like saying that in World War 2, the French were "traitors to their fellow Europeans" because they accepted aid from the United States and Canada to win their country back from the Germans.
More realistically: There's both a moral, or perhaps public relations, question, and a raw power question.
Regarding raw power, there's the obvious point that, despite all I've said above, the more Indians there were, the harder it would have been to defeat them. Yes, when it came to raw violence, the Europeans had the advantage of superior military technology. But they also had to travel long distances to fight, and they had to supply their armies over long distances. They were fighting in unfamiliar terrain while the Indians were in their homeland. Etc. Even if the Europeans had the raw power to win in the long run, as their death toll mounted, at some point they might well decide that it just isn't worth it. Like the collapse of the British Empire after World War 2, or the recent U.S. withdrawal from Iraq, or the Roman evacuation of the British isles ca AD 400. There have been many times in history when a big nation has the raw numbers and military might to defeat a weaker nation if they were willing to pay the cost in money and lives ... but they're not willing.
RE morals: To Europeans, America was largely an empty continent open for the taking. The more Indians there were, the less viable this view would have been. While some Europeans had no qualms about massacring any Indians who got in their way, others had great respect for the Indians. In Columbus diary he describes the Indians as being pure and virtuous people because they were untainted by the evils of civilization. When one tribe told him that another were cannibals, he refused to believe that it was possible, writing in his diary that this must be a mistake, that now and then someone got lost in the woods and his family came up with wild stories about him being eaten by cannibals to explain why he never returned. The Pilgrims executed one of their own people for murdering an Indian. Etc. I think it's fair to say that the bloodier any conquest was, the more moral objections that would have been raised to it.
So wow, where does all that rambling lead? It would almost surely have slowed down the European conquest. I think it's unlikely that it would have prevented Europeans from having any foothold in the Americas at all. After all, some of the early Spanish conquests were before the plagues really took hold. My gut feel is that, if enough Indians had survived, there could still be independent Indian nations today in the Great Plains of North America, maybe in Argentina and Brazil. But the Spanish would still have taken the Aztec and Inca empires and the U.S. would still be established east of the Mississippi. There'd still be white people in California, though who they'd be aligned with politically is hard to say.