The basic premise is that the real value of government debt must equal the discounted expected future primary surpluses of the government. Should the government acquire debt beyond its capacity to repay, bond holders will realise this, selling the bonds down, which drives up interest rates. As a sovereign cannot default on debt denominated in its own currency, the central bank is forced into buying these bonds, expanding the money supply, and boosting prices until the point where the nominal debt becomes repayable.
The big argument about this theory is whether the `fiscal limit', described above, is an equilibrium condition determining prices, or a limit on government behaviour. Roughly, Christopher Sims, Michael Woodford, and John Cochrane have argued the `equilibrium condition' line, while Willem Buiter has argued the fiscal limit is a `constraint'.
Both of these arguments are, though, difficult to logically justify.
The first---that the price level is implicitly determined by the stock of government debt relative to expected future budget balances---is easy to defeat. The problem with this thesis is that it requires all government savings to be made in the expectation of some future primary deficit. Should one government ever run a fiscal surplus despite having noexpectations of future primary deficits, then (without some further strong assumptions) the model fails.
The second---that the fiscal limit defines the maximum borrowing a government could make before provoking inflation---is more complicated to argue. Assuming the Buiter argument is true implies governments could lend money continually without ever expecting to run a primary deficit. This is irrational, and violates what is known as the "no-Ponzi-game" condition, which forbids actors from either holding positive or negative balances at the day of reckoning (which occurs into the infinite future). Therefore, the Buiter hypothesis necessitates assuming one of the main actors in models only behaves irrationally: a very strong assumption. Or is it?
This raises a question:
For any actor that has an infinite life and expects never to deplete their savings, are their savings irrational? Remember---infinity periods is a very long time. Can a government be a Ponzi-lender?