Technical debt isn't just a startup thing. It's ever-present in tech organizations. Technical debt is probably a leading factor in the irrelevance and ultimate death (typically sale / merger) of most software companies. The product gets increasingly buggy over time as developers pile on more and more hacks to get features out the door without writing down the debt, and customers move on to competitors that have fewer bugs. This is what happened to Netscape, for example.

For startups, technical debt can show up as unreliability (remember Twitter's fail whale?), or it can sink a product before it ever becomes famous enough for you personally to remember.