The argument goes that long-term trends that improved corporate profits at the expense of consumption led to a structural crisis devastating the economy. Corporate profits, in the face of weak consumer demand, was then fueled into speculative activities such as the stock market. The stock collapse was made worse by these firms pulling out their investments, and long-term recovery was fueled by the gradual expansion of consumer demand through government supported efforts.
The recourse to "shares" of income doesn't appear very causally important, as it ought to be the levels of consumption and corporate profits that matter, rather than their relative ratio--though it may be useful as a marker for those constituent changes. But leaving aside the explanatory power of the consumption and corporate profit story with respect to the Great Depression, it doesn't seem like a great way to explain today's problems.
One reason is that it misses consumer holdings of assets. Many people before the Depression of course held stocks, and the collapse in asset value spurred additional saving. Similar things are happening now, as consumers smoothed their consumption by relying on the increase in their home value (and stocks, to a lesser extent) to finance additional spending. The drop in home and stock values are going to reverse the massive indebtedness of the average American household, and the resulting drop in spending will make it much harder to come out of the recession. Certainly the share of corporate profits (in retrospect, inflated due to asset bubbles and leverage) to consumption has been rising. But household consumption has also done well lately--the problem in fact being that consumption was too high, fueled by debt collateralized over overpriced assets.
It's not clear either that stocks were overpriced because corporations faced weak consumer demand and instead blew profits on speculative investments. Some may have, but by and large it appears that thrifty corporations saved cash, while consumers splurged.
The broader picture, however, of weak consumer demand, and corporate profits chasing speculative investments with low rates of return do seem to be present in various Asian countries. As James Surowiecki notes, the enduring cheapness of Japanese stocks is fueled by the depth of the fall from overpriced asset values in the 1980s, thrifty Japanese consumers, and bad corporations. Return on equity is notoriously low in Japan, as companies rely on cheap debt funneled from sister companies to make value-destructive investment decisions. It's really becoming apparent that Japanese corporate structure is not really capitalist (as someone pointed out, it's the only Communist country that has worked) but rather works to maximize the interests of corporate insiders.
Another place where you are seeing something of this pattern play out is China. Krugman some time ago was skeptical of the productivity of the Chinese economy, claiming that it was instead fueled through expanding inputs. Since then, it's clear that labor productivity has played at least some role, but recently the picture is more mixed. Consumption remains low as a portion of GDP; the bulk instead goes towards investment or (much smaller) exports. A powerful case has been made that the Chinese economy is becoming less capitalist, rather than more.
The argument goes that Chinese growth in the last few decades was dominated by small-medium enterprises, many of them local. Growth recently has been capital intensive, and dominated by state-owned enterprises. The banking system is filled by bad loans and provides easy credit to flailing politically-connected firms. The most salient consequence is the wholescale devastation of the landscape from Beijing to Shanghai--commissar command of the economy results in undervaluing natural resources, which are cheaply converted as inputs. Energy and water efficiency are horribly low, even comparative lto other countries.
Speculative investments have also dominated the landscape. Real estate was valued highly, as was the stock market. Company investment in equities resulted in vicious circles (my company's value depends on the earnings of other companies, who are also invested in my company's stock...). So large part of the recent boom is probably fictional, a relic of the hunger of state-owned-enterprise for overinvestment and speculation. The image of capital investment--skyscrapers, factories--is impressive, but really not as relevant from a capitalist point of view as the return on investment. Now, it turns out that a lot of this investment is worth less, while of course much of the export-oriented facilities is endangered. Shifting to more domestic consumption is the obvious next step, and that's presumably the way things are going to head.
It's hard to imagine the political consequences of necessary adjustments. Everyone says "growth down into the single digits," but one hedge fund guy I've talked to expects a falling economy. The long-term growth potential is clear, but recent and future growth is looking much more tenuous. This is obviously a problem, given the lack of ways of political expression. The Tibet riots came out of nowhere; doubtless others are mad about the falling stock market, health safety failures, a collapsing housing market, and looming economic issues.