Professional worriers and cultural conservatives in the U.S., including highbrow tribalists like Samuel Huntington, like to rant and rave about the coming horde of Latin Americans (most Mexicans) who will swamp America's Anglo-Saxon culture and English language in a rising tide of Spanish culture and linguistic mixing. Yet, traditionally, Mexico (with, even today, a third the population of the U.S.) has worried more about Americanization than the U.S. has worried about Mexicanization. Indeed, one can argue that "North Americanization" has become an ever-stronger force in Mexican society over the last twenty years or so. (The situation in Canada is similar in some ways, although Canada's population is only a tenth of America's and most Canadians live within 100 miles of the border, so Canadians tend to guard their culture even more jealously.)
There has never been a North American identity comparable to the identity that (some) Europeans feel. NAFTA has increased economic integration within North America, and further integration is highly likely (e.g., as a result of improved transit links). But that doesn't mean Canadians, Americans, and Mexicans feel much devotion to a common identity of any kind. Both academics and NGOs are studying these issues, and even the President of Mexico has blessed Americanization (perhaps more in hopes of garnering campaign contributions than anything else). Yet there are important differences between Canadians, Americans, and Mexicans on questions of values and ideology, so it is unclear how far North American integration will proceed.
One interesting issue is, I think, the possible emergence of greater cooperation between particular regions of North America, irrespective of existing national borders -- think the Pacific Northwest from Vancouver to Portland, the Rocky Mountain West from Calgary to Denver or even Chihuahua, the Desert Southwest from Phoenix to Hermosillo, "greater Texas" from Dallas to Monterrey, "greater New England" from Connecticut to Nova Scotia, and so on. These regions may have common economic and environmental issues and to some extent more of a common culture than national surveys would indicate. There already exist multiple forums for regional cooperation, and I expect more to emerge.