In many ways the biggest problem facing transportational cycling is recreational cycling.
Most cycling facitlities are designed with recreational cyclists in mind -- even though the primary funding source in the US is the federal Department of Transportation, which insists that recipients certify (wink, wink) that the facilities are primarily transportational in nature. From a purely numerical standpoint, it makes sense. There are something like 100 million recreational cyclists and perhaps 3 million transportational cyclists in the US.
While recreational cyclists want to have fun, transportational cyclists want to get somewhere useful. In general, when someplace usefule exists, other people want to go there as well, and they go by car, so there is a road that goes there. What transportational cyclists generally want is just to be able to use the existing roads.
From an advocacy perspective, there is an important difference as well. Transportation is a right, ensconced in common law, the constitution, and federal and state laws. Recreation is an amenity. So transportational advocacy is largely about access and enforcement of rights, and recreational advocacy is largely about agitating for facilities.
These two types of cycling don't always work at cross purposes, but sometimes they do. The classic example is recreational advocates arguing for facilities because the roads are too dangerous, which provides ammunition to those who would ban cyclists from the roads.