WASHINGTON — It has become the trillion-dollar question: can President Obama find that much in spending cuts and tax increases to keep his campaign promise to overhaul the health care system, without adding to already huge deficits? Mr. Obama and the Democrats running Congress are deeply split over the possibilities.

House and Senate leaders do not like his ideas but cannot agree on alternatives. Other proposals that could reduce health care spending would take too long to show savings for purposes of Congress’s budget scorekeeping, and many would require big investments initially, such as for research into cost-effective treatments.

Meanwhile, special interests like insurance companies, employers and even sugar beet and corn growers are on alert to oppose anything that could hurt them.

Adding to the pressure, Republicans are back to attacking Democrats as tax-and-spenders. Yet they have not proposed how to pay for their own, more modest health care proposals. Nor did they offset the cost of creating the Medicare prescription drug benefit six years ago when they controlled Congress and held the White House. Its projected deficits exceed the shortfall for all of Social Security over the next 75 years, according to the program’s 2009 trustees report.

For some time, lawmakers and lobbyists privately assumed Mr. Obama would not hold the fiscal line for a deficit-neutral bill. Instead, he has reinforced it. Legislation “must and will be paid for,” he said in a news conference on Tuesday.

Worries about the economy hardened Mr. Obama’s resolve, administration officials say. “There’s a concern that if Congress were to pass a big health care bill that was heavily deficit-financed, financial markets could react negatively, with higher interest rates that could deepen the recession,” said Robert Greenstein, the executive director of the liberal Center on Budget and Policy Priorities, which supports the administration’s goal of a deficit-neutral health care overhaul.

Even so, each idea to cut spending or raise taxes has political pitfalls. A review of the options — and how dug in the opponents are — shows just how hard it will be for Mr. Obama to reshape the health system. Here are snapshots of major proposals:

¶Limit income-tax deductions for high earners. This is Mr. Obama’s main idea for raising revenue, but Congress is not likely to pass it except in a greatly scaled-down form.

He proposed to collect a projected $267 billion over 10 years by making taxpayers in the top income tax brackets, now 33 percent and 35 percent, deduct their mortgage interest, state and local taxes and charitable donations at the 28 percent income tax rate. Democratic leaders immediately objected that that would hurt charities, universities and other entities dependent on tax-deductible donations, as well as taxpayers in high-tax cities and states, including New York City and other places home to Democratic leaders.

Mr. Obama has not given up. He counters that a 28 percent itemized deduction rate for top earners would be the same as under President Ronald Reagan. Just 1.4 percent of households would be affected, the nonpartisan Tax Policy Center reported. The Center on Philanthropy at Indiana University says charitable giving would decrease 2 percent.

Any compromises would raise less revenue than Mr. Obama proposed. One alternative would exempt charitable contributions from the 28 percent limit. That, however, would provoke governors from high-tax states or Realtors and bankers protective of the mortgage tax break to press for exempting the other categories as well.

Another idea would maintain the 33 percent and 35 percent rates for itemized deductions after the Bush tax cuts for the rich expire in 2011, when the top two income tax rates revert to 36 percent and 39.6 percent. That would leave the current break for deductions unchanged, but prevent it from becoming relatively more generous when income taxes rise for affluent taxpayers.

Even that fallback hit a wall in the Senate Finance Committee. The opposition of Senator Charles E. Grassley, the panel’s senior Republican, carries weight with Senator Max Baucus, the Democratic chairman from Montana, who is determined to produce a bipartisan bill. Both men say any tax increases or cost savings should come from the health sector. Their preference is to make the value of workers’ employer-provided health benefits subject to income taxes.

¶Tax employee health benefits. While House Democrats are opposed, the support of influential senators for taxing some benefits and the huge sums to be raised ensures that this option will be part of the debate. And Mr. Obama does not rule it out, though he opposed such a tax as a presidential candidate and promised that only the top 5 percent of Americans would see an income tax increase under his administration.

The numbers underscore why this is both the most lucrative and the most controversial among the financing options. Taxing all employer-provided health benefits as income would raise more than $2.5 trillion over a decade — more than twice Mr. Obama’s goal. And employer-provided insurance is the largest source of coverage for Americans, benefiting about 160 million employees and their dependents under age 65.

Most economists favor ending the tax break. They argue that it mainly goes to upper-income taxpayers and discourages cost-consciousness among consumers, thus encourages excessive spending on health care. Many Republicans also oppose the tax break, as did some senior Obama advisers, including Peter R. Orszag, the budget director, and the economist Jason Furman, before they joined the administration.

But its supporters include unions, which are a force in the Democratic Party and count tax-free health benefits as a legacy of the labor movement, as well as many businesses eager to attract and retain valued employees with good benefits. The opponents of taxing job-related health benefits cite analyses projecting that several million Americans could lose insurance if the tax break were repealed and some employers dropped coverage.

The senators are not suggesting repealing the tax break. Instead, they want to cap the value of benefits that go untaxed. For example, if the tax-free limit is $13,000, an employee with a policy worth $15,000 would pay income taxes on $2,000.

But the cap proposal does not satisfy opponents who say that it could penalize taxpayers in areas with high medical costs. One potential compromise is to avoid the controversy altogether and instead impose an income-tax surcharge on the wealthiest taxpayers.

¶Spend less on Medicare. Roughly two-thirds of the $948 billion in savings that Mr. Obama has proposed over 10 years would come from a range of reductions in projected Medicare spending. Those would mean lower payments to hospitals and other health care providers as well as insurance companies, inviting opposition from some of the country’s most formidable lobbies.

The biggest savings he proposes, $177 billion, would come from having insurance companies bid for government reimbursements for offering private plans, known as Medicare Advantage, to senior citizens. The administration also has proposed to cut $106 billion in subsidies to hospitals that serve many uninsured patients, arguing that fewer Americans would lack coverage after overhauling health care. And it says $110 billion could be cut by reducing payments to hospitals and doctors generally to reflect productivity gains.

The Senate Finance Committee is working to reduce Medicare and Medicaid payments over time to a range of industries — insurance companies, hospitals, doctors, drug makers, nursing homes, home health care companies and medical device makers — arguing that all of them stand to benefit from overhauling health care, with more paying customers.

¶Increase behavior-changing “sin taxes.” Congressional analyses show that more than $200 billion over 10 years could be collected from new or increased taxes on sugared soft drinks, tobacco products and alcoholic beverages implicated in common health problems like obesity and cancer. Yet while the options are on the lawmakers’ table, Senator Baucus has said they are on “life support.”

The Joint Committee on Taxation calculated that a 3-cent tax on each 12-ounce sugared soda would raise $51.6 billion over a decade. But opposition is not limited to the bottling industry. Major sources of sweeteners include Montana, which has a large sugar beet industry, and Iowa, which produces high-fructose corn syrup — the home states of Senators Baucus and Grassley.

The government could raise $61.5 billion with an additional alcoholic beverage tax that would mean about 40 cents more for a fifth of liquor, 48 cents for a six-pack of beer and 49 cents on a bottle of wine. Advocates point out that federal alcohol taxes were last raised in 1991; adjusted for inflation, they are 37 percent lower now. But local wineries and microbreweries now operate in nearly every state, suggesting that major distillers will not be the only opposition.

Each of these taxes is often criticized as regressive, meaning it would disproportionately affect lower-income people. But proponents counter that the poor have the most to gain from universal health coverage.

A version of this article appeared in print on June 26, 2009, on page B1 of the New York edition.