In what is now the East Coast of the United States, for example, the Indians OUTNUMBERED the newcomers until about 1648 ~ that's when a particularly bad winter combined with a slightly higher than normal incidence of several communicable diseases (probably could add in the flu to the situation), boosted the death rate among Indians and Europeans right through the roof.
The big difference between the two groups wasn't natural resistance ~ it was far simpler ~ Europeans could ship in an indefinite resupply of human beings, which they promptly did.
There are a number of good books on the market that cover the American population catastrophe of the 16th and 17th centuries.