Is there a threshold we can pass in terms of debt-to-GDP that will cause a runaway sort of effect?
No there is no threshold or magic number (at least not one we know of). Few years ago there was an influential research claiming that there is a threshold at about 90% debt-to-GDP ratio published by Reinhart and Rogoff where debt was supposed to start having strong negative effects on growth, but that research was discredited later on when it was discovered it was based on several mistakes in their calculations (see Herndon et al 2014).
As the literature currently stands, there are no arguments for some 'magic' number. Debt can start being a problem for a country at 30-50% debt-to-GDP, but it might be no problem at all even at 300% of debt-to-GDP. It all depends on the structure of debt (e.g. who holds the debt?), how the debt is denominated (i.e. does country borrow in its own currency or foreign one?), and also what is the long term debt trajectory (e.g. see Pescatori et al 2014). The debt trajectory is very important because even country with large debt can out-grow it since debt-to-GDP ratio is literally ratio of $\frac{\text{debt}}{GDP}$ and thus you can reduce it both by reducing debt, or by keeping debt constant and growing GDP or just making sure debt does not grow as fast as GDP.
However, while there is no magic threshold for debt crisis/overhang high debt can have serious negative effects at some point (although for US it is likely quite high so you should not necessarily worry about scaremongering of some politicians. Japan that is somewhat similar (high income, industrial and aging country), is able to sustain debt-to-GDP in excess of 250% - see Statista data here).
What are these supposed effects?
This will depend on the nature of debt crisis once it is triggered. Although the Reinhart and Rogoff work on debt threshold was discredited, rest of their work which describes negative effects of debt crises is actually still quite solid. Reinhart and Rogoff show that debt crises are often having following negative effects:
- high inflation (especially when we talk about external default on debt denominated in their own currency), in worst case scenario it can lead to currency collapse and currency substitution
- banking crisis
- capital flight
- facing higher interest rates in the aftermath
- lower economic growth
- being forced to reduce some fiscal spending
However, note not all countries will suffer from all of the above problems. Some of the above problems are policy choices, others depend on exact structure of debt. Its difficult to say what would happen to the US so I won't speculate on that.
