I found this entry on Wikipedia:
Bicycling has been a popular mode of transportation in Davis for decades, particularly among UC Davis students.
Bicycle infrastructure became a political issue in the 1960s, culminating in the election of a pro-bicycle majority to the City Council in 1966. By the early 1970s, Davis became a pioneer in the implementation of cycling facilities. As the city expands, new facilities are usually mandated. As a result, Davis residents today enjoy an extensive network of bike lanes, bike paths, and grade-separated bicycle crossings. The flat terrain and temperate climate are also conducive to bicycling.
In 2005 the Bicycle-Friendly Community program of the League of American Bicyclists recognized Davis as the first Platinum Level city in the U.S. In March 2006, Bicycling magazine named Davis the best small town for cycling in its compilation of "America's Best Biking Cities." Yet bicycling appears to be on the wane among Davis residents. From 1990 to 2000, the U.S. census reported a decline in the fraction of commuters traveling by bicycle, from 22 percent to 15 percent.
From this article and from what I have previously heard and read about Davis, the cycle infrastructure is extensive enough to rival that of Amsterdam. However, a modal share of 15 percent is just slightly higher than that of Portland (8 percent, where most riders ride on city streets, although many are traffic-calmed bike boulevards). Irvine, CA has "44.5 miles (71.6 km) of off-road bicycle trails and 282 miles (454 km) of on-road bicycle lanes", but my understanding is that its modal share is incredibly small. I wish I could find an exact percentage -- most of what I have heard about Irvine is anecdotal, namely former residents saying that it was almost unheard of for people to use the bike paths for commuting or errands.
I don't feel like looking up the exact ridership of Copenhagen and Amsterdam right now, but I know it is somewhere between 40-50 percent. These are also colder and rainier cities.
Irvine and Davis seem to demonstrate that "if you build it, they will come" is only true up to a certain point -- you will get diminishing returns upon your investment unless there is some other factor encouraging people to bike.
The only other factors that I can think are the expensive parking, narrow streets, high cost of car ownership, and high energy prices that you find in European cities. If oil prices permanently shoot up to $200+ in the U.S. due to global demand outstripping supply, maybe our modal share will rival that of Europe. In that case, all we really have to do is wait -- bike specific infrastructure won't be necessary then, as the roads will become more hospitable due to fewer motorists (who will in turn be forced to modify their driving habits due to more cyclists).
(As a disclaimer, I don't really align myself with either the vehicular cyclist or "built a s**t ton of specialized infrastructure" side of the debate. I take more of a minimalist stance, namely that bike boulevards combined with bike/ped shortcuts and bridge paths are the most inexpensive and cost-effective form of infrastructure, and that they aren't based upon the utopian vision that we could persuade the majority of the population to cycle without economic necessity forcing them to.)