On the projects I have been involved so far, some technical debt has been "paid" (managed) only at the beginning of new phases of the projects, i.e. after "big releases" or milestones.
A very important aspect about technical debt is that it not only involves developers but management as well. In that sense, I am aware that the best way to deal with it, is to make it visible to "non-technical project stakeholders" who might allocate time and resources to manage the technical debt once they understand its implications.
This article discusses several types of technical debt, which ones might be healthy, and specially how to manage and track the technical debt load.