WASHINGTON — As a candidate in 2020, Joseph R. Biden Jr. campaigned to end billions of dollars in annual tax breaks to oil and gas companies within his first year in office.It’s a pledge he has been unable to keep as president.Mr. Biden’s budget request to Congress this week was his fourth attempt to eliminate what he called “wasteful subsidies” to an industry that is enjoying record profits.“Unlike previous administrations, I don’t think the federal government should give handouts to big oil,” Mr. Biden said after his inauguration. His new budget proposal calls for the elimination of $35 billion in tax breaks that would otherwise be provided to the industry over the next decade.Mr. Biden’s wish is opposed by the oil industry, Republicans in Congress and a handful of Democrats. In Washington, it seems, oil and gas subsidies are the zombies of the tax code: impossible to kill.“Everybody agrees fossil fuel subsidies are wasteful, stupid and moving things in the wrong direction,” said Michael L. Ross, a political science professor at the University of California, Los Angeles who studies fossil fuel tax breaks. “Getting rid of them seems to be one of the hardest things to achieve on the climate agenda.”The oil and gas industry enjoys nearly a dozen tax breaks, including incentives for domestic production and write-offs tied to foreign production. Total estimates vary widely; environmental groups take a broad view of what constitutes a subsidy while the industry hews to a more narrow definition. The Fossil Fuel Subsidy Tracker, run by the Organization for Economic Cooperation and Development, calculated the total to be about $14 billion in 2022.Two of the biggest tax breaks have been in place for about a century.The oldest, known as “intangible drilling costs,” was created by the Revenue Act of 1913 and was aimed at encouraging the development of U.S. resources. The deduction allows companies to write off as much as 80 percent of the costs of drilling, things like employee wages and survey work, in the first year of operation, even before producing a drop of oil.Another subsidy, dating from 1926 and known as the depletion allowance, initially let oil companies deduct their taxable income by 27.5 percent, a number that seemed strangely specific.“We could have taken a 5 or 10 percent figure, but we grabbed 27.5 percent because we were not only hogs but the odd figure made it appear as though it was scientifically arrived at,” Senator Tom Connally, the Texas Democrat who sponsored the break and who died in 1963, was quoted as having said in “Sam Johnson’s Boy, a Close-Up of the President From Texas,” a biography of Lyndon B. Johnson.That tax break proved so lucrative it prompted celebrities like Jimmy Stewart, Frank Sinatra and Bing Crosby to become oilmen on the side, buying interests in oil wells and using the deduction to shelter their Hollywood income.The allowance was eliminated in 1975 for large producers and reduced for smaller companies, which are still allowed to deduct 15 percent of their revenue from their taxable income.Early on, lawmakers justified the deductions by saying they would help attract investors to oil drilling, which could be a risky venture. After all, not every well strikes oil.Today, Exxon Mobil and Chevron, the largest U.S. energy companies, are enormously profitable. Last year, American companies pumped 13 million barrels each day on average, a record that had made the United States the largest crude oil producer in the world, according to the U.S. Energy Information Administration. The country is also the world’s leading exporter of liquefied natural gas.The oil and industry is expected to reap $1.7 billion in 2025 from the intangible drilling tax break, and $9.7 billion over the next 10 years, according to the White House. It is expected to realize $880 million in benefits from the depletion allowance tax break in 2025, and $15.6 billion by 2034.Instead of investing in their businesses, the oil and gas companies have poured profits into “stock buybacks, mergers, and acquisitions that benefited executives and wealthy shareholders,” the Biden administration said on a fact sheet accompanying the budget proposal.The two tax incentives together have increased the expected value of new oil and gas projects by billions of dollars in most years and as much as $20 billion in years when the price of oil was high, according to a 2021 study by the Stockholm Environment Institute, a research organization.A New York Times analysis of lobbying reports found that energy companies have spent more than $30 million since Mr. Biden was elected on lobbying efforts that included preserving the intangible drilling and depletion allowance tax breaks. The U.S. Chamber of Commerce, which spends more than $100 million annually in lobbying on a wide range of issues, also cited energy tax breaks on its lobbying reports.Ending subsidies for oil and gas is not a new idea, but it has never gotten far.President Barack Obama tried in almost every budget to scrap the tax breaks but failed, even when Democrats controlled both the House and Senate from 2009 to 2011.Among the Democrats who have fought to preserve the subsidies has been Senator Joe Manchin III of West Virginia, the state that is ranked second for coal production and fourth for natural gas. In the House, Representatives Vicente Gonzalez Jr. and Henry Cuellar, both Texas Democrats, implored party leaders in 2021 to maintain the subsidies. They were joined by Filemon Vela Jr., a Democrat who also represented Texas in the House at the time.Mr. Manchin said this week that Congress had enacted tax incentives for both clean energy and fossil fuels and that coal, oil and gas should not be singled out for changes.“The Biden Administration and their radical climate advisers have disregarded common sense by requesting Congress remove these incentives before we accomplish an energy transition that doesn’t sacrifice reliability and affordability,” Mr. Manchin said in a statement.Oil executives reject the term “subsidy” to describe the tax policies. They argue that most industries enjoy tax deductions and oil companies write off just a sliver of what they pay in federal taxes.They also point out that federal subsidies for wind, solar and other forms of clean energy are rapidly expanding. The Energy Information Administration found that about 46 percent of federal energy subsidies between 2016 and 2022 were associated with renewable energy.Anne Bradbury, chief executive officer of the American Exploration & Production Council, called Mr. Biden’s call to change the tax code “a direct attack on American energy production” that would harm an industry that supports more than 9 million jobs.“This budget should not even receive a vote in the House or Senate, and lawmakers in both chambers should craft budgetary policy that does not impede American energy production,” Ms. Bradbury said in a statement.Senator Lisa Murkowski, an Alaska Republican, dismissed Mr. Biden’s request to end tax breaks as messaging aimed at young climate activists. “Do I think it’s going to go anywhere? No,” she said.The debate over semantics aside, the result is that the government is helping to artificially lower the price of producing oil, gas and coal in a way it does not do for other manufacturers, economists said.“It’s just corporate welfare,” said Joseph Aldy, a professor at the John F. Kennedy School of Government at Harvard University who served as a special adviser to President Barack Obama on energy issues.Others note the irony of continued government support for fossil fuels at a time when scientists say nations must rapidly transition away from oil, gas and coal to cut the carbon emissions that are driving climate change.Congress has a “fiscal and moral responsibility to stop taxpayer dollars from padding the profits of an industry that is destroying our planet,” said Senator Bernie Sanders, Independent of Vermont.Last year nearly 200 countries signed a global accord at the United Nations climate summit in Dubai, United Arab Emirates, to move away from fossil fuels and eliminate “inefficient” subsidies for coal, oil and gas. The United States was among the signatories.