To some, it is a tax on blue-state liberalism. To others, it eliminates a costly perk for the wealthy.

To many, however, the federal deduction for state and local taxes is a cherished break that can save them thousands of dollars in double taxation.

President Trump and House Republicans are making the latest push to end the provision. Yet the elimination is anything but certain, because it challenges longstanding tradition and powerful opponents, including Republican and Democratic officials in wealthy and populous states like California, New Jersey, New York and Texas.

“I don’t think they’re going to seriously restrict it at all,” said William G. Gale, a co-director of the nonpartisan Urban-Brookings Tax Policy Center and a former economic adviser to President George H. W. Bush.

Congressional Republicans have indicated they plan to go it alone on tax legislation. But taking on such an entrenched interest usually requires bipartisan support.

“If Republicans do it by themselves, they put a big target on their backs,” Mr. Gale said. Members of Congress generally take a “political Hippocratic oath” to “never be seen to do obvious harm,” he said, but eliminating the deduction, which would raise taxes and undermine the ability of cities and states to tax, would violate that precept.

A raft of organizations that represent state and local governments — including the National Governors Association, United States Conference of Mayors and the National Conference of State Legislatures — quickly denounced the measure, saying it would upset the balance between local and federal interests and undermine growth. “We fundamentally believe that Americans’ income, property and purchases should not be taxed twice,” the organizations said in a statement.

The idea of preventing the federal government from taxing money that citizens must pay to state and local tax collectors goes back to the Civil War, and was eventually included in the first income tax legislation. One fear, articulated by the founding fathers in the Federalist Papers, was that the federal government might try to monopolize taxation “to the entire exclusion and destruction of state governments.”

Striking a blow at the taxing power of cities and states has long appealed to conservative Republicans. They argue that the deduction works like a subsidy and encourages states — particularly those dominated by Democrats — to set higher rates and spend more taxpayer money.

The deduction is also one of the code’s most expensive items. According to a 2016 report from the Tax Policy Center, ending of the deduction would save the federal government $1.3 trillion over 10 years.

That money is particularly tempting because most of the other big-ticket items in the tax code — including the deduction for mortgage interest and charitable contributions — have been labeled off limits by the White House and House Republicans.

The total cost of the president’s tax-related wish list is still a mystery, given the scarcity of detail, but deep cuts in corporate and individual taxes certainly would leave a gaping budget deficit that could run into the trillions.

Like most other deductions, the state and local tax provision primarily benefits wealthier taxpayers who itemize deductions. The Tax Policy Center’s report finds that households with annual incomes exceeding $100,000 would bear roughly 90 percent of the increase; those with incomes over $500,000 would absorb 40 percent. More precise calculations are impossible because other proposals — like eliminating the alternative minimum tax — would create other savings for some of these taxpayers.

For example, roughly 30 percent of taxpayers itemize deductions, but that number would certainly fall if the standard deduction were increased, as Mr. Trump proposed, or a variety of breaks were erased.

While the upper middle class will feel the biggest hit, the wealthiest will be mostly unaffected because of upper limits on the value of deductions, said Edward D. Kleinbard, a professor of tax law at the University of Southern California. “People affected are those with six-figure incomes, not seven-figure incomes,” he said.

What is clear is that residents in states that impose the highest combination of property taxes, and individual and corporate income taxes will pay the most. Taxpayers in 10 states — California, Illinois, Maryland, Massachusetts, New Jersey, New York, Ohio, Pennsylvania, Texas and Virginia — claim more than half of the total deducted, according to the Tax Policy Center. Though residents even in some states with low income taxes, including Florida, Nevada and Washington, also benefit because they can deduct general sales taxes instead, the center said.

The Partnership for New York, an association of large employers, estimated that the value to New York City taxpayers of itemized deductions for state and local taxes was $7.7 billion in 2014, or about $6,600 per affected taxpayer. For those earning more than $200,000, the average deduction for state and local taxes was more than $30,000. Pressure to reduce local taxes is likely to result in less spending on programs and services, economists say.

Conservatives have complained that the deduction causes low-tax, often poorer, states and regions to subsidize high-tax areas.

But as Kathryn S. Wylde, president of the partnership, pointed out, even with those deductions, New York City still sent far more money to the federal government than it received back. City residents paid $96 billion in personal income taxes, and businesses paid $19 billion. In return, the city received about $61 billion from Washington.

Other interest groups have also registered their opposition, like the National Association of Realtors, which said eliminating the state and local deduction would help to “nullify the current tax benefits of owning a home for the vast majority of tax filers.”