How is the FDIC funded? Assuming it is funded by the banks, will the increase in the FDIC limit increase what the banks pay and will that cost be passed on to all depositors regardless of the size of their deposits?
Your assumption for FDIC funding is 100% correct. The insurance premiums are paid by participating banks in the system.
The increase in FDIC deposit coverage will not affect consumers directly right away. Insurance risk is spread around depending on claims submitted.
Just like all home owners who cary flood insurance in coastal flood plains were affected by hurricane damage two years ago in the gulf coast...all banking customers will be affected. The cost of the increased FDIC coverage will not be limited to depositors only, but all customers who utilize banking services.
Banks, (and more importantly their shareholders) expect a certain return on their investment. If a bank's margins are reduced by the higher premiums, they will need to off-set that loss through some other revenue generation. Generally, this would be higher fees or loan costs to all customers, not just depositors.