From the FDIC press release:
The Federal Deposit Insurance Corporation (FDIC) today announced publication of its final rule regarding company-run stress testing required by the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010. The rule applies to covered institutions with total consolidated assets greater than $10 billion.
The FDIC Board today also approved a final rule that refines the deposit insurance assessment system for insured depository institutions with more than $10 billion in assets. The final rule amends the definitions used to identify concentrations in higher-risk assets to better reflect the risk posed to institutions and the FDIC. As of June 30, 2012, there were 108 institutions with more than $10 billion in assets.
The new rule on deposit insurance assessment could affect deposit rates of large banks. Higher payments may be required from large banks that hold riskier assets. That could put downward pressure on deposit rates from these large banks.This Bloomberg article
has more discussion on this new regulation.