Go high enough, interest payments consume the entire federal budget. There is no way out except revenue growth (infeasible without breakthrough productivity improvements), taxation, and printing money (equivalent to taxation). Before that point, other bad things happen such as creditors losing faith in the government, making debt more expensive and destabilizing the dollar's position as global reserve currency.
Over the last few decades, debt has continued to rise as a percentage of the federal budget, and appears that trend will continue without drastic action.