I don't get this. I don't understand why we would assume that pre-crisis demand was supported by or in any way dependent on higher levels of indebtedness.
I have a sense for what the story is (or one story is). Imagine (if you can) that America has experienced steady growth in income inequality, which has effectively concentrated an ever larger share of income in the hands of households with a lower marginal propensity to consume. Other things equal, such a shift in the income distribution will reduce demand and require a lower real interest rate to match desired saving with desired investment. The Federal Reserve, conscious of the need to keep demand near potential, dutifully pushed down its policy interest rate in an effort to reduce real interest rates (and was successful). This encouraged non-rich households to take on ever more debt, the better to generate higher levels of investment, mostly in the form of single-family homes. It simultaneously encouraged yield-conscious rich households to seek ways to channel their savings, via new financial products, into higher yielding debt instruments. Desired saving and desired investment balanced through the magic of Wall Street wizardry and everyone made out like bandits until the world nearly ended. Now, the Fed is trying to balance desired saving and desired investment once again, but it is finding it difficult to do. In part this is because deleveraging continues, but it may also be because new financial rules are blocking the flow of credit from rich households to non-rich, which is necessary to restore adequate demand.
Does this story make sense? I'm not so sure. Part of the difficulty is in knowing what is driving what. But let's consider one thing. The trend in private-sector indebtedness moves very closely with the trend in America's current-account balance.