The idea is finicky. How can a poor country like India and other Asian countries, which are perenially short of cash to deal with their own problems, finance a rich country like United States. But a little common sense and a bit of economics will explain this fallacy. All we need to do is to take a look at the current accounts of US and other Asian countries. A current account, in simple terms, is just an account of money being spent and received by a country (which is basically the government of that country). As it stands, the Asian economies are running a current account surpluses since last few years. It means that the asian economies are earning more as compared to their expenses. The new export led growth policy being followed by the asian economies has contributed greatly to this current account surplus. Now, add this surplus with the huge capital inflow that is taking in Asian economies. These two things together imply that all the Asian central banks have a huge pile of dollar (more exports, less imports, increasing FDIs, all mostly in dollars). So what do the central banks do with this huge pile of dollars. They invest in US securities which are extremely low yield
Now lets have a look at US. The government under Bush has been on a spending spree. After all, the wars and the deep tax cuts given to the rich do not come free. These policies have ensured that the US government has a huge current account deficit, or in other words, the govt is spending far more than it is earning. But from where it is getting the dollars to spend? This is where the investments from the Asian countries come handy. The developing countries have been parking the excess dollars with them in US securities. This gives US easy access to a very inexpensive source of capital. So the govt there is hardly bothered about its current account deficit.
What does all this mean? There are quite a few implications. Firstly, this whole dependence on dollar, assigning it almost the status of an international currency means that while developing countries work hard to generate and save capital, United States can affort to spend it recklessly and inefficiently. Secondly, investing in US securities primarily means that the moment dollar collapses, all the US securities held by Asian banks loose value or become worthless depending upon how bad is the fall. Thirdly and most importantly, by treating US as a central bank of the world, the Asian countries ensure that they will do everything possible to avoid a default by this central bank as their economy's health becomes tightly coupled with that of US. Somebody who understands this and who is in a position of power in US (like the US president) can easily use this to bulldoze other countries to fall in line with its own agenda.
So what is the recourse? An idea would be for the Asian economies to invest forex reserves in different central banks to spread their risks. This is happening but on a very miniscule level. The other thing would be the idea of an international currency. An organization like World Bank, with the representation and voting power structure rationalized, can be the governing body for the international currency. In a truly globalized and connected world, there is no place for so many currencies. The world of finance needs to speak in one language.