Apparently, having to ride right alongside motor vehicle traffic, is a big reason many people in the U.S. won't even consider riding a bike very far on a road where motor vehicles travel also. Cycle-tracks, generally being distance separated from main lanes of a road, address this issue.
The preferred form of cycle track in Denmark is contiguous to the road and separated only by a small crub or ramp. Ironically, the Danes prefer this type of infrastructure because its safer than full separation when there are lots of intersections of driveways.
The expense and effort to build one likely would not force the city where it was sited, to go into bankruptcy. Portland has survived complications associated with constructing the Tram, Streetcar, Max. A first class cycle-track on Foster would be miniscule in comparison to those projects.
Cycling has far less fiscal support than mass transit. Moreover, building cycle tracks (unless they are funded by the State or Feds) will almost certainly slow the development of cycling connectivity. Hembrow and other european cycling advocates argue that increasing connectivity is more important than installing a particular form of infrastructure. I agree.