Everyone knows the US debt bill is incredible, however, it is largly debated whether or not this is a long-term problem, most economists from my understanding beleive it is of little concern. If the debt is generating returns in excess of the IR, then its no problem. This is a hugely debated topic though, and you will find numerous articles on the web about it. In the short-term however, or even the medium-term, this will have absolutely no effect on a stock market crash\correction. Infact, any problem due to this debt level would not be seen until the very very distant future.
A private equity deal to flop? What exactly do you mean? Most loan defaults and bank troubles, would come from an increasing IR in the US, and an inability for all the property market mortage holders to pay back the banks. Though, the banks are all backed (the large ones), so a bank collapsing is very seldom seen, and the large banks are partically impossible to collapse.
IR will not go up a lot more, but why would an IR fall induce a bear market? Quiet the opposite.
If the US market crashes, no doubt the Chinese economy will also struggle, and our commodity sector will implode.
Though, from those IMF reports, it appears the world economy is stable for the short-term at least, with only a minor slowdown in growth.