Obama plays cowboys and Indians
That unyielding spirit is what defines us as Americans. It is what led generations of pioneers to blaze a westward trail.
This statement makes an identification between Americans and westward-blazing pioneers*. But think about what those pioneers were doing -- they were driving out a set of Americans who were already there. In Obama's message Native Americans are not Americans, they're part of the adversity that real Americans needed an "unyielding spirit" to overcome. They fall in the same category here as the British and the Great Depression, plus our current wars and economic troubles (Obama's other brief examples of adversity overcome by America). That is, if they're there at all -- the pioneer narrative often makes Native Americans disappear altogether, leaving a wilderness that's hostile because of its pristineness. Perhaps next year Obama could praise the "unyielding spirit" that "led generations of pioneers to blaze a westward trail, and led generations of native people to resist those pioneers and rebuild their culture in a greatly changed country." It would be an interesting trick to acknowledge the US as an agent of colonialism on the very day that we celebrate our narrative as the country that threw off colonialism in 1776.
*You could also construct a pioneer narrative for Asian and Latin@ Americans, though their trails were blazed mostly eastward and northward respectively.