NEW YORK — Could a limit on the fees retailers pay on debit card purchases cause your bank or credit union to fail? That’s the dire picture some are painting as a cap on so-called swipe fees nears.

An attempt to delay the start of a cap on the amount banks and payment processors, such as Visa and MasterCard, can charge merchants for handling debit transactions failed to pass the Senate on Wednesday. That means the Federal Reserve will go ahead and implement the rule, part of last summer’s financial regulatory overhaul.

The Fed has proposed a 12-cent cap for each debit purchase, a sharp cut from the average 44 cents retailers now pay. The regulator must issue a final version of the rule, which will take effect on July 21, in the next few weeks in order to give banks and processing networks the time to comply. It is possible that the 12-cent cap could change before the rule is finalized.

The industry estimates that as much as $14 billion in revenue could be lost.

Jim Blake, CEO of HarborOne Credit Union in Brockton, Mass., was hoping the Senate would approve the delay, which would have also required study of the cap’s impact on community banks and credit unions.

Although there’s an exemption in the law for institutions with market capitalizations less that $10 billion, Blake, like many of his counterparts, does not think it will work.

“You saw every community bank and credit union around the country join together in opposition of this,” said Blake, whose credit union has a market cap of $1.85 billion. “That doesn’t happen too frequently.”

The National Association of Federal Credit Unions said the average cost for each debit transaction for its members is 35 cents.

Small institutions have several complaints about the law:

* It doesn’t include any language about how the small-bank exemption will be enforced.

* There’s no way to prevent stores from asking customers at the register to use cash, or a different debit card from a bigger bank that is subject to the fee cap.

* It allows retailers to decide which networks process their transactions, taking that decision away from banks, which currently choose the network. That leads to the expectation stores will choose the networks that charge the least, rather than those that charge the higher fees for smaller banks.

* The proposed cap of 12 cents doesn’t factor in certain bank costs, such as fraud prevention or the fees banks pay to the networks.

Sen. Dick Durbin, the Illinois Democrat who sponsored the law, disagrees about the potential for the small bank exemption. “We believe that legal protection, together with the forces of the market, will help them,” he said. “I’ve done my best to give them special treatment because they’re in special financial circumstances.”

The senator said merchant groups have pledged not to reject small bank debit cards, and scoffed at the idea that the networks will encourage retailers to use lower-cost options.

Tim Chen, the founder of credit card search site NerdWallet.com and a former analyst who followed card networks, said they have strong incentives to offer two levels of pricing — one for large banks and one for smaller. The networks make a lot more money under two-tiered pricing, because they’re still capturing the old fees from the exempt smaller banks, he said.

Durbin said the banking industry is upset because its “dirty little secret” is now public. Before the debate, swipe fees were invisible, he said, but now it’s well known that the payment networks collect billions each year in fees that retailers pass on to their customers.

If the exemption doesn’t work and revenue does drop sharply for small banks and credit unions, they’ll have to resort to the same sort of steps that larger banks are taking. That may mean charging for checking accounts and perhaps instituting annual fees for debit cards. Credit union profit margins are already so tight, said Fred Becker, president of the National Association of Federal Credit Unions. “They’re anticipating an erosion here of their fees and a pretty significant erosion.”

As an example, Harbor Credit Union collected $2.7 million in debit income last year, or roughly 3 percent of total revenue. Blake is unsure how much of that he’ll see going forward.

The industry will continue to press regulators and Congress on the issue.

Durbin pledged to revisit the issue if the exemption doesn’t work. “We want to make sure these banks and credit unions survive.”