A better question is: Where would it have come from? Most of the assets backing money market funds are short-term obligations to repay from a broadly diversified range of borrowers, usually corporate or municipal, with a small amount of cash to facilitate transactions. The terms of those loans to companies and local governments don't allow the bank to just demand the money ahead of schedule. The assumption is that when one particular fund experiences a high volume of withdrawals, it will be able to sell its commercial-paper assets to other banks, or as a last resort, borrow from the Fed to cover the withdrawals. The extraordinary event here was that there was such a massive panic across the entire country, not even the Fed would have been able to keep up.
Incidentally, what touched off this panic was when two money market funds "broke the buck" on the same day; that is, instead of paying their investors an interest dividend, they announced that their investors' deposits had shrunk (by a small amount) from the day before. Depositors thought the financial crisis was about to consume money market accounts, panicked, and moved their cash from non-FDIC-insured MM accounts into regular checking accounts.
The funds would have simply vaporized. The actual supply of green dollar bills in the world is about $800 billion. But money market funds are valued at $8 trillion. If everyone actually tries to redeem their shares for dollars, each share would ends up being worth pennies on the dollar.
Instead, the Fed stepped in an backed up the funds with the full faith and credit of the U.S. government. Essentially, the Fed monetized the money market funds.
Incidentally, what touched off this panic was when two money market funds "broke the buck" on the same day; that is, instead of paying their investors an interest dividend, they announced that their investors' deposits had shrunk (by a small amount) from the day before. Depositors thought the financial crisis was about to consume money market accounts, panicked, and moved their cash from non-FDIC-insured MM accounts into regular checking accounts.