The Federal Deposit Insurance Corporation insures bank accounts so that depositors (not investors) do not get wiped out if a bank goes under through no fault of their own. It was instituted during the New Deal because so many families lost everything when their life savings in their bank accounts followed their failed banks into oblivion. If FDIC can't meet its obligations in the event of widespread bank failure, millions of families who saved their money and played by the rules, who didn't play the market or speculate on real estate, will be wiped out.

FDIC, like all insurance, is funded by premiums, which are paid by the banks. If FDIC goes, there is no place where you can put money where it is safe except under the mattress, and it might just lead to a run on the banks, or, to use the current euphemism, a "loss of confidence" in the banking system.