FDIC members pay for FDIC insurance based off of FDIC assessments (which is roughly based on amount of liabilities in the bank). The bigger the bank, the more they pay for FDIC insurance.
Again, I'm not sure if its a very direct line to "American Taxpayers". FDIC insurance is paid for by banks directly. By being generous to your perspective, I can argue that these costs are passed onto the depositors (ie: anyone with a bank account). But personally speaking, my bank account balance is high enough that I don't pay any fees, though I can imagine that a number of people do pay banking fees.
So what paid for this, were the various fees that you paid to your bank. (Which in my case, is $0 directly, though banks like Bank of America obviously skim off of the interest rates, at least a little bit).
So I can see the argument that Americans (who by and large own bank accounts) are at least in the pool of money that goes into FDIC insurance. But the direct payments are from the banks themselves, and its only an indirect fee at best that ties the typical American to this whole process.