WASHINGTON — Senate Democrats on Tuesday, bowing to an aggressive lobbying campaign by the banking industry and pushback from Republicans, scaled back a Biden administration plan for the Internal Revenue Service to try to crack down on tax cheats.

The new proposal, which would help pay for the expansive social policy and climate change bill that includes it, narrows the scope of information that banks would have to provide to the I.R.S. about customer accounts. Under the revised plan, which is backed by the Biden administration, banks would be required to provide data on accounts only with total annual deposits or withdrawals worth more than $10,000, rather than the $600 threshold that was initially proposed. The reporting requirement would not apply to payroll deposits for wage and salary earners or to beneficiaries of federal programs such as Social Security.

The plan was narrowed after a steady lobbying campaign by banks and a barrage of criticism from Republicans, who argued that the administration’s desire to bolster the I.R.S. to shrink the $7 trillion “tax gap” amounted to an invasion of privacy and government overreach.

Senators Ron Wyden of Oregon, chairman of the Finance Committee, and Elizabeth Warren, Democrat of Massachusetts, accused detractors of lying to protect affluent tax cheats. But their decision to pull back the initial proposal showed how legislation containing measures that Democrats believed only weeks ago would be politically unassailable — from cracking down on rich tax scofflaws to allowing the government to negotiate lower drug prices — could succumb to challenges from well-financed opponents. With no votes to spare in an evenly divided Senate, opponents need to change just one vote to doom a provision in the social policy bill.

Critics of the proposal have incorrectly suggested that the I.R.S. would be tracking information about individual transactions. The administration has said the I.R.S. would not monitor specific customer transactions but instead use the account information to spot discrepancies between it and what individuals reported on their tax returns.

“Banks and their wealthy clients are outright lying, saying they would see individual transactions, and Republicans are backing them up,” Ms. Warren said.

The Biden administration insists that audit rates for those making less than $400,000 would not go up and that the program was focused on collecting unpaid taxes from the rich.

But Republicans, who have expressed distrust of the I.R.S. for years, continued to criticize the proposal as an invasion of privacy. It is familiar ground. In the 1990s, Republicans orchestrated well-attended hearings on I.R.S. abuse that portrayed the agency as out of control. In 2013, Republicans accused the I.R.S. of targeting conservative groups, although the political targeting crossed party lines.

“Whether it’s $600 or $10,000, under this proposal, the intimate financial details of everyone in this room — at a minimum, of every American who has a job — will be turned over on a daily basis to the I.R.S.,” Senator John Kennedy, Republican of Louisiana, told reporters, despite the proposal’s exemption of payroll deposits. “What could possibly go wrong?”

Senator Kevin Cramer, Republican of North Dakota, warned darkly, “Marx is at the doorstep.”

Mr. Wyden called the Republican accusations a flat-out “lie” promulgated by lawmakers at the behest of “donors and allies” who “want nothing more than a crippled I.R.S. unable to go after their cheating.” Under the revised plan, instead of daily transaction reports, banks would send “two numbers once per year,” Mr. Wyden said, “the total amount going into an account, and the total amount going out of it.”

But the campaign has taken its toll. The Treasury Department said the Biden administration would back the narrower proposal because the I.R.S. already had information about American workers and retirees. While it would give the agency visibility into far fewer bank accounts, the Treasury said in a fact sheet on Tuesday that “only those accruing other forms of income in opaque ways are a part of the reporting regime.”

“Today’s new proposal reflects the administration’s strong belief that we should zero in on those at the top of the income scale who don’t pay the taxes they owe, while protecting American workers by setting the bank account threshold at $10,000 and providing an exemption for wage earners like teachers and firefighters.” Treasury Secretary Janet L. Yellen said in a statement.

“The main reason Republicans have latched on to this issue as the one to lie about every day is because they know their tax agenda is a political loser,” Mr. Wyden said. “The American people overwhelmingly want to ensure megacorporations and billionaires pay their fair share, so Republicans have largely given up on their tired trickle-down arguments.”

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

The Treasury Department has estimated that its original proposal to require banks to report account balances, along with plans to beef up the enforcement staff at the I.R.S., could raise $700 billion over a decade.

In a letter to House Democrats last month, Ms. Yellen urged lawmakers not to water down the information-reporting proposal. Originally, that part of the plan was projected to raise $460 billion over a decade. The Treasury Department estimated that the narrower plan that Congress had been considering could raise between $200 billion and $250 billion over that time.

The department believes that those are conservative estimates and that the “deterrent effects” of the policies could still generate $700 billion of additional tax collection in the next decade.

Republicans continued to raise the possibility that any new reporting rule would expand to target lower-income taxpayers. Senator Michael D. Crapo of Idaho, the ranking Republican on the Finance Committee, pointed to an analysis by Congress’s nonpartisan Joint Committee on Taxation that estimated that half the unpaid taxes came from taxpayers making less than $50,000 a year.

Taxpayers earning at least $500,000 are hiding only 4 percent to 9 percent of the money that could be recovered by a crackdown in tax cheating, Mr. Crapo said.

Mr. Wyden said that analysis was dated and was crippled by the committee’s inability to track how much money was owed to the I.R.S., especially by those using complicated tax schemes like multilayered partnerships and multiple bank transactions, which the new reporting requirements would target.

He cited testimony on Tuesday by the deputy Treasury secretary, Wally Adeyemo, who estimated that the wealthiest 1 percent of taxpayers will fail to pay more than $2 trillion in taxes that they owe over the next 10 years.