Banks are hoping to win at least a small reprieve from the Federal Reserve on Wednesday when the central bank releases a final proposal cracking down on the fee banks charge retailers when a debit card is used.

Bank officials are not expecting the Fed to back off much from its December proposal, but even boosting the fee cap by a few cents would ease the blow.

In December the Fed proposed capping the fees at about 12 cents per transaction -- a 75 percent cut from the 2009 average of 44 cents, according to the central bank.

The proposal was greeted with cheers by retailers and groans by bankers.

The 12-cents-per-transaction cap would cost banks about $14 billion annually, according to credit card comparison website CardHub.com.

Bank officials said the best they can expect on Wednesday is for the Fed to boost the cap to about 20 cents per transaction by including the cost of fraud protection and other costs banks argue were not adequately included in the December proposal.

We would be surprised if this went north of 17, said Richard Hunt, president of the Consumer Bankers Association.

A research note from Goldman Sachs said that investors are expecting the Fed to boost the cap slightly.

If the Fed does not meet these expectations and keeps the cap at 12 cents banks stocks could take a short-term hit, the note says.

Sanford C. Bernstein senior analyst Rod Bourgeois said in a note that investors are expecting the cap to be boosted to 17 cents to 18 cents.

The crackdown on swipe or interchange fees is required by the 2010 Dodd-Frank financial oversight law.

On Wednesday banks lost a legal challenge to the law.

The U.S. Court of Appeals for the Eighth Circuit affirmed a district court's denial of a motion to block the Fed from issuing its rule.

The motion was sought by the banking unit of TCF Financial Corp , which is arguing the fee crackdown is not constitutional.

That suit will now continue in the U.S. District Court, District of South Dakota.

Retailers are hoping the fierce lobbying they have done will counterbalance whatever ground financial services lobbyists have gained with the Fed.

It would be surprising to us if it came below the 7-12 cent number and it would be disappointing if they moved beyond the 7-12 cent number on the high side, said David French, senior vice president of government relations for the National Retail Federation.

The lobbying battle has been vigorous, with retailers charging that the current system is a boon to big banks like Bank of America and Citigroup .

Banks push back by arguing the crackdown will pad the profits of retail giants like Wal-Mart Stores and Target Corp with customers seeing none of the savings.

Beyond the transaction cap, the Fed is due to decide how it will enforce a requirement aimed at making the card network market more competitive and whether it will attempt to make an exemption to the fee cap for small banks more explicit.

The changes were to have gone into effect July 21 but the Fed is expected to find a way to give banks more time to be in compliance with the debit fee cap.

The Dodd-Frank law requires the Fed to prevent banks and card companies, like Visa and MasterCard , from restricting how many networks can be used to process a debit card transaction.

Banks and card networks are hoping the Fed will choose the simplest option it laid out in December -- requiring a debit card to be carried over only two unaffiliated networks.

Small banks, those with less than $10 billion in assets, are exempt from the debit fee cap but they have argued they don't believe it will work in practice.

Community banks are hoping the Fed will issue language laying out how card networks will make the exemption work, said Viveca Ware, a senior vice president at the Independent Community Bankers of America.

(Reporting by Dave Clarke in Washington and Brad Dorfman in Chicago; Editing by Tim Dobbyn and Phil Berlowitz)