The United States rolls over its debt on a scale of a few years, not every day. So the "run on the dollar" would play out over a year or two rather than overnight. Furthermore, I have described for clarity a sudden one-time loss of confidence. The actual process of running from the dollar, however, is likely to take more time, much as the European debt crisis has trundled along for more than a year. In addition, because prices tend to change relatively slowly, measured inflation can take a year or two to build up after a debt crisis.
Like all runs, this one would be unpredictable. After all, if people could predict that a run would happen tomorrow, then they would run today. Investors do not run when they see very bad news, but when they get the sense that everyone else is about to run. That's why there is often so little news sparking a crisis, why policymakers are likely to blame "speculators" or "contagion," why academic commentators blame "irrational" markets and "animal spirits," and why the Fed is likely to bemoan a mysterious "loss of anchoring" of "inflation expectations."