When the Biden administration looked for ways to pay for the president’s expansive social policy bill, it proposed raising revenue by cracking down on $7 trillion in unpaid taxes, mostly from wealthy Americans and businesses.

To help find those funds, the administration wants banks to give the Internal Revenue Service new details on their customers and provide data for accounts with total annual deposits or withdrawals worth more than $600. That has sparked an uproar among banks and Republican lawmakers, who say giving the I.R.S. such power would be an enormous breach of privacy and government overreach.

Banks and their trade groups are running advertising and letter-writing campaigns to raise awareness — and concern — about the proposal. As a result, banks from Denver to Philadelphia say they are being deluged with calls, emails and in-person complaints from both savers and small-business owners worried about the proposal. JPMorgan Chase & Company has issued talking points to bank tellers on what to tell angry customers who call or come into a branch to complain.

“We have heard a lot from our customers about their concerns about their privacy,” said Jill Castilla, the chief executive of the one-branch Citizens Bank of Edmond, just outside Oklahoma City. “I’ve gotten calls, emails, and then we’ve had many customers come in.”

Banks already submit tax forms to the I.R.S. about the interest that customer accounts accrue. But the new proposal would require they share information about account balances so that the I.R.S. can see if there are large discrepancies between the income people and businesses report and what they have in the bank. The I.R.S. could audit or investigate the gaps to see if those taxpayers are evading their obligations.

Biden administration officials say the United States needs more information from taxpayers to crack down on those who do not pay what they owe. The measure, which would affect more than 100 million households and millions of businesses, is estimated to capture $460 billion in additional revenue over a decade, primarily from the wealthiest Americans.

“This is a very serious policy proposal,” Treasury Secretary Janet L. Yellen said at a congressional hearing last month. “We have a $7 trillion estimated tax gap that we have a great deal of tax avoidance by individuals and businesses — typically very high-net worth, high-income individuals and businesses that have opaque sources of income that are not paying the taxes that are due.”

Treasury officials say the effort is not about tracking individual transactions and is not aimed at lower- or middle-class households. The $600 threshold was chosen to weed out accounts that are generally dormant or get little use, such as children’s accounts, while still giving the government the broadest possible visibility. Administration officials say audit rates for taxpayers who earn less than $400,000 per year will not go up.

“This is about making sure the top 1 percent can’t evade $160 billion per year in taxes,” said Alexandra LaManna, a Treasury Department spokeswoman.

Top Democrats say that empowering the I.R.S. is key to making the economy more fair. Senator Elizabeth Warren of Massachusetts has warned that the I.R.S. is handicapped when it comes to tracking the income of the wealthiest.

“The kinds of income that the I.R.S. has the least visibility into are the kinds of income that are overwhelmingly concentrated among the very richest taxpayers,” Ms. Warren said. “Strengthening information reporting, as well as providing protected and sustained I.R.S. funding, would ensure that we focus enforcement on the biggest fish.”

But the pushback is putting pressure on the Biden administration to scale back the proposal. Lawmakers are discussing raising the required disclosure level to $10,000 rather than $600, a Treasury official said, and making taxpayers who are paid through payroll-processing companies exempt from the required reporting. The Treasury estimates that could reduce the amount of money it could recoup to about $210 billion over a decade.

The outcry over the proposed measures stems in large part from a carefully planned lobbying campaign by the banking industry, which has spent months raising awareness and opposition to the plan in cities and towns across the country.

Banks say the reporting requirements would raise their costs and put them in the unenviable position of handing customer information over to the I.R.S.

Top industry trade groups have hammered the proposal in emails and phone calls to members. They have argued their case in meetings with senior administration officials, including Ms. Yellen and Charles P. Rettig, who runs the I.R.S. They established a social media hashtag, #KeepMyBankingPrivate, that some executives have used in sharing their doubts about the proposal.

“We proudly join @ICBA and others in telling Congress that we serve our customers, not the IRS,” Bankcda, whose main branch is in Coeur d’Alene, Idaho, wrote in a recent Twitter post tagging the Independent Community Bankers of America, a trade group that caters to smaller banks and is helping to lead opposition to the measure.

After the initiative made its first appearance deep in the Treasury’s annual budget proposal in May, the American Bankers Association said it and its state-level partner groups quickly heard from hundreds of member banks, raising questions about the idea and its implications. The Independent Community Bankers of America began flagging the potential changes to its members, prompting many of them in turn to alert their customers.

Trade groups also helped gather signatures for a Sept. 17 letter to congressional leaders complaining about the proposal.

“Indiscriminate, blanket data collection would amount to a troubling effort to profile American taxpayers based on account characteristics without grounds for suspicion of tax evasion,” the letter argued. It was signed by more than 40 business groups, including the Mortgage Bankers Association, Global Cold Chain Alliance and Foodservice Equipment Distributors Association.

Awareness of the proposal has been amplified by ad campaigns, conservative news media coverage and Facebook posts, including one that caught the attention of Crystal Causey, a 39-year-old advertising account executive in Los Angeles.

“I wouldn’t allow my husband or my parents to monitor my bank account activity,” she said in an email. “There’s no way I would be OK with the government monitoring it.”

Industry representatives say it is unusual to see banks communicate with their account holders on a political matter. “This is the first time in 20 years that I’ve seen that banks have reached out to inform their customers on an issue” like this, said Paul Merski, who runs congressional relations for the community bankers association.

Jim Reuter, the chief executive of FirstBank near Denver, said concerns about the potential provisions have bubbled up frequently, including over a coffee he had with a small-business owner in early October.

“Their upshot is, ‘I pay my taxes, so why would you be sending additional information to the I.R.S.?’” Mr. Reuter recalled. “I said I agree with them. We’re in the trust business. And it just goes without saying that sending the customer’s information somewhere without giving consent — that’s not what we do as a bank.”

The proposal’s critics have said the I.R.S. appears ill-equipped to process and safeguard such an overwhelming amount of data to actually catch cheats.

“I have to tell you the proposal that has been put forth about expanding the amount of information that the I.R.S. is going to get on private bank accounts has been something I’ve been asked about at parks, at grocery stores, at convenience stores around the district,” Representative Trey Hollingsworth, Republican of Indiana, told Ms. Yellen at the congressional hearing last month. “This has people deeply afraid about the emergence of an apparatus that can be used against them.”

J.P. Freire, a spokesman for Representative Kevin Brady of Texas, the top Republican on the House Ways and Means Committee, said Texans were “terrified” of the I.R.S. and that his boss was fielding inquiries about the proposed disclosures from at least three or four constituents every week.

Ms. Castilla, the community banker in Oklahoma, said a local schoolteacher had stopped by her office two weeks ago to share her anxieties about the idea of the government peering into her financial records. She told the teacher she believed the proposal was an overreach, Ms. Castilla recalled, and added that banking associations and Oklahoma’s congressional delegation were fighting it.

Even if the dollar threshold were raised to $10,000, Ms. Castilla said, it would still be onerous for her bank. “This would require a massive amount of infrastructure,” she said.

Treasury officials say they are flummoxed by the outrage, given that banks of all sizes initially told them they could comply with the rules, which would not take effect until 2024.

“They have made clear during conversations with banks that firms can easily implement a simple proposal like the one under consideration in Congress, and that any compliance costs would be minimal,” said Ms. LaManna, the Treasury spokeswoman.