If people came through the bering strait, wouldn't north America have had more time and opportunities to develop further than the south?
Aside from the problems inherent in the idea of 'civilization' I can confidently say that the people of North America did actually develop civilization as you have defined it.
The big ones are obviously the Maya and the Triple Alliance(Aztecs). Since Mesoamerica is generally considered a part of North America they qualify. I am assuming you actually mean Canada and the continental United States when you say North America though.
With that in mind I can still say that North America did, in fact, have civilizations! Lets look a just a few I can remember. This is by no means an exhaustive list, just what I can recall right this second.
The first, and in some ways best, example is the Mississippian culture in the southeast. They created monumental architecture in the form of highly engineered mounds as well as a number of cities. The largest of these is Cahokia near modern-day St. Louis. They also had extensive trade networks reaching throughout the continent.
To the southwest we have the Pueblo peoples. They built some truly massive structures out of adobe. Large 'grand houses', temple complexes and cliff dwellings are what they are known for. You want infrastructure? They managed fairly intensive agriculture in a very unforgiving area as well as having numerous roads in the modern four corners area, mostly New Mexico.
In the northeast we can look at the Haudenosaunee/Iroquois Confederacy for an example of a complex, large scale political organization. While they may not have had any particularly large urban areas that I am aware of they had a kind of political organization that could be mistaken for a modern nation. There are some historians who think that they may have had a strong influence on the development of the US government, though there is a fair amount of debate about that.
Source: Pretty much all of this comes from 1491 by Charles Mann supplemented by browsing wikipedia for the links and to refresh my memory of some specifics.