At his State of the Union address this year, President Biden celebrated the fact that his new climate and tax law would no longer allow some of America’s largest corporations to pay zero in federal taxes.

“Because of the law I signed, billion-dollar companies have to pay a minimum of 15 percent,” Mr. Biden said, referring to the Inflation Reduction Act of 2022. “God love them.”

The new corporate minimum tax was one of the most significant changes to the U.S. tax code in decades. Its logic rested on the idea that rich companies should not be able to find loopholes and other accounting maneuvers in order to pay lower tax rates than their workers.

But making the tax operational has become a mammoth challenge for the Biden administration, which has faced intense lobbying from industries that could be on the hook for billions of dollars in new taxes. Those groups have been flooding the Treasury Department with letters asking for lenient interpretations of the law and trying to create new loopholes before their tax bills come due next year. Republican lawmakers have been trying to repeal the law while Democrats such as Senator Elizabeth Warren of Massachusetts have been urging Treasury Secretary Janet L. Yellen to enforce it strictly.

The legislation, which passed with no Republican support, called for the corporate minimum tax to take effect in the 2023 tax year, meaning it will apply to corporate profits earned this year. But the tax was only loosely defined, and Treasury is still writing the rules that will determine how it is carried out.

The corporate minimum tax is entirely separate from the 15 percent “global minimum tax” that the Biden administration brokered with more than 140 nations in 2021. That agreement was aimed at stopping large multinational companies from seeking out tax havens and forcing them to pay more of their income to governments. While the deal is moving ahead in other nations, it continues to face obstacles in the United States, where Congress has been unable to ratify the agreement and allow the U.S. to comply with the global rules.

But Democrats were able last year to pass a domestic corporate minimum tax, which is a revival of a policy that was last employed in the 1980s. It captures tax revenue from companies that report a profit to shareholders on their financial statements, known as book income, while bulking up on deductions to whittle down their tax bills.

While the corporate tax rate stands at 21 percent, many large companies pay far less than that to the federal government. For years, big companies such as FedEx, Duke Energy and Nike have been able to take advantage of various deductions and tax strategies so that they effectively owe nothing in federal taxes. A 2021 report from the Institute on Taxation and Economic Policy found that 55 of the nation’s largest companies had paid no federal income tax the previous year.

An analysis by the Joint Committee on Taxation last year found that about 150 companies with tax rates below 15 percent would be subject to the new tax. Companies like Amazon and Berkshire Hathaway, which have had effective tax rates in the single digits in recent years, could face the biggest increases in their tax liabilities, according to a summary of research about the impact of the tax published by the Congressional Research Service.

At the Berkshire Hathaway annual meeting in May, Warren E. Buffett, the company’s chief executive, acknowledged that there was uncertainty over the new tax but said he did not oppose it.

“We can figure out ways, once we know the rules, where we will pay the 15 percent tax,” Mr. Buffett said.

While the tax is aimed at some of the largest companies, smaller businesses have also expressed concern that they could be swept into the new tax regime if the regulations are not sufficiently clarified.

In a comment letter to the Treasury Department and the Internal Revenue Service this year, CenterPoint Energy, a public utility company based in Texas, said it could be unfairly targeted because it had sold part of its gas pipeline and storage operation. Even though CenterPoint paid taxes on the sale, the gains could raise the company’s revenue enough to require it to pay additional money under the corporate alternative minimum tax.

“CenterPoint is neither a large corporation nor a corporation that did not pay its fair share but is being subjected to the C.A.M.T. as a result of transactions that reduced its business operations,” the company wrote. “The incongruity of the result is striking.”

The Treasury Department is expected to release the final rules for the tax before the end of the year. It already made concessions to the insurance industry, which raised concerns that the tax could upend its business model, and told companies that they would not be responsible for making quarterly tax payments related to the new minimum until all the regulations were clarified.

“Treasury is working to ensure that the biggest and most profitable corporations pay their fair share and that the corporate alternative minimum tax is workable and administrable,” said Ashley Schapitl, a Treasury spokeswoman.

The 15 percent minimum tax applies to corporations that report annual income of more than $1 billion to shareholders but reduced their effective tax rate well below the statutory 21 percent. It was projected to raise over $200 billion over a decade.

Businesses that might face the new tax have been spending heavily to shape its scope and minimize their exposure.

According to Accountable.US, a nonpartisan watchdog group, large financial firms and industry groups representing international conglomerates spent more than $1 million during the first half of this year lobbying Congress over the corporate minimum tax and a 1 percent stock buyback excise tax that was also included in the Inflation Reduction Act. Accountable.US described that as a “significant” amount since Republicans already oppose the provision.

Many sectors are bracing for the tax’s potential impact, but energy companies, the film industry, financial firms and foreign companies that operate in the United States are particularly concerned, according to a review of comment letters submitted to the federal government and corporate filings.

“We’re trying to figure out how to add up apples and oranges, if you will, to make sense of it,” said Nancy McLernon, president and chief executive of the Global Business Alliance, which represents international companies that have U.S. subsidiaries.

Ms. McLernon, whose organization has a working group trying to ensure that the new tax rules can work alongside international accounting standards, lamented that the measure had only made things more complicated for businesses that invested in the United States.

I.R.S. tax forms, which allow for an array of deductions, and financial statements shown to shareholders present different pictures of a company’s performance. Investors use a firm’s book income to get a clearer view of the health of a business; however, some analysts have suggested that companies may soon start to take steps to obscure that measure.

Big businesses that will be hit by the tax are now trying to figure out what kind of income will put them over the $1 billion threshold and what deductions they may be able to keep.

When the legislation passed last year, Senator Kyrsten Sinema of Arizona persuaded her Democratic colleagues to preserve a valuable deduction, known as bonus depreciation, that is associated with purchases of machinery and equipment. Since then, businesses that spend money on repairs and maintenance of their equipment have tried to make the case that those expenses should be included in that carve-out. Other firms, such as film companies, have tried to make the case that the cost of making movies should still be deductible from the new tax.

Despite all the lobbying, most companies are still trying to figure out how the tax will work and how much they need to worry.

“Anybody who is within the scope of the corporate alternative minimum tax has some pretty meaningful unanswered questions,” said Pat Brown, co-leader of PwC’s Washington National Tax Services practice and a former Treasury official.

Tax and accounting experts have warned for years that this type of corporate minimum tax would not be easy. They contend that it creates a new tax base and has the potential to encourage companies to change how they report their financial income to seek out new loopholes.

William McBride, the vice president of federal tax policy at the Tax Foundation, which has been critical of the new minimum tax, said it had been difficult to set up because it was misguided in the first place. He argued that trying to marry accounting rules and tax laws was a recipe for confusion.

“It’s not clear if it’s even resolvable in a way that’s going to satisfy taxpayers such that they’re not stuck with enormous compliance costs,” Mr. McBride said.

Efforts to overturn the tax will be fruitless while Mr. Biden is in office, but that hasn’t stopped Republican lawmakers from trying.

Backed by lobbyists from the National Association of Manufacturers, the National Mining Association, the U.S. Chamber of Commerce and the Western Energy Alliance, Senate Republicans introduced legislation in May to repeal what they described as a “reckless and complicated” tax that targets job creators.