WASHINGTON — President Obama went before a convention of receptive but wary doctors on Monday to make the economic case for a health care overhaul, both for the nation and for the physicians’ own bottom lines.

But as the president spoke at the annual conference of the American Medical Association in Chicago, it became clear that one of the major health plans on the table would cost at least $1 trillion over 10 years yet leave tens of millions of people uninsured.

Congress is wrestling with how to pay for Mr. Obama’s vision to extend health care to all Americans, and some lawmakers are considering tax increases and spending cuts different from the ones he has proposed. House Democrats, for example, are weighing a tax on soft drinks and a value-added tax, a broad-based consumption tax similar to the sales taxes many states levy.

An analysis released Monday by the nonpartisan Congressional Budget Office raised the hurdles for draft legislation in the Senate just as its Health, Education, Labor and Pensions Committee planned to begin voting on Wednesday. The office concluded that a plan by the committee’s Democratic leaders, Senators Edward M. Kennedy of Massachusetts and Christopher J. Dodd of Connecticut, would reduce the number of uninsured only by a net 16 million people. Even if the bill became law, the budget office said, 36 million people would remain uninsured in 2017.

That finding came as a surprise. Robert D. Reischauer, an economist who headed the budget office when Congress tackled the health care issue in the Clinton administration, said that if so many people remained uninsured, it might not be feasible to cut special federal payments to hospitals that serve many low-income people.

Mr. Obama said Saturday that the government could save $106 billion over 10 years by cutting such hospital payments as more people gained coverage.

Senator Orrin G. Hatch of Utah, a senior Republican on both committees drafting health legislation, said he found the office’s numbers stunning. He calculated that the Kennedy bill would cost taxpayers $62,500 per uninsured person over the 10 years.

Mr. Obama took the cost issue head on in Chicago. “The cost of inaction is greater,” he told the doctors, because rising health care prices are “an escalating burden on our families and businesses” and “a ticking time bomb for the federal budget.”

Opening a week in which health care will dominate attention in Congress, the president’s speech on Monday was the latest example of an oft-used ploy to press his case: appearing before skeptical audiences, confident of his powers of persuasion but willing as well to say what his listeners do not want to hear.

Mr. Obama spoke just days after the A.M.A. had signaled opposition to his proposal for a public health insurance plan to compete with private insurers as part of a menu of choices, much like the one for members of Congress.

“The public option is not your enemy,” Mr. Obama said. “It is your friend, I believe.” Saying it would “keep the insurance companies honest,” the president dismissed as “illegitimate” the claims of critics that a public insurance option amounts to “a Trojan horse for a single-payer system” run by the government.

Mr. Obama twice referred to the use of such “fear tactics” about “socialized medicine” in past legislative battles, without pointing out that the A.M.A., a traditionally Republican-leaning group, was among those using the charge, as in the mid-1960s debate over creating Medicare for people 65 and older.

Mr. Obama drew repeated applause, and even some standing ovations, when he called for incentives to get more medical students to go into primary care instead of the more lucrative specialty practices, and when he pledged to work with doctors to reduce their often unnecessary “defensive medicine” to avoid malpractice lawsuits. But scattered boos met his follow-up remark that he opposed any cap on malpractice awards.

The president’s emphasis on reducing health care costs over expanding insurance coverage, which dates to his campaign, reverses Democrats’ priorities of recent years. Obama advisers say the focus on cost savings has appeal for all Americans, not just the uninsured. Some advisers, including veterans of the Clinton administration, say President Bill Clinton’s emphasis on covering the uninsured helped doom his health care plan in 1994.

“We have made cost control a coequal objective, just as important as the expansion of insurance coverage, which has traditionally been the dominant goal for Democrats,” said Rahm Emanuel, the White House chief of staff. “The entire discussion has to be centered on controlling or reducing costs.”

That rationale has been Mr. Obama’s answer to those who, after his election, predicted that he would have to shelve his campaign promise to overhaul health care to attend instead to an economy in crisis. “If we fail to act, premiums will climb higher, benefits will erode further, the rolls of the uninsured will swell to include millions more Americans, all of which will affect your practice,” he told the A.M.A. members.

The practical problem for Mr. Obama is that by all accounts, the savings and efficiencies he envisions will not occur quickly, certainly not in the 10-year time frame of budget scorekeeping for purposes of passing legislation.

The budget office estimated that 39 million people would get coverage through new “insurance exchanges.” But at the same time, it said, the number of people with employer-provided health insurance would decline by 15 million, or about 10 percent, and coverage from other sources would fall by 8 million.

In effect, the office said, millions of people would get a better deal if they bought insurance through an exchange because they could qualify for federal subsidies not available if they stayed in their employers’ health plans. Subsidies are expected to average $5,000 to $6,000 a person.

Mr. Obama assured skeptics in the audience: “You did not enter this profession to be bean counters and paper pushers. You entered this profession to be healers. And that’s what our health care system should let you be.”

On Wednesday, leaders of the Senate Finance Committee hope to unveil what will be the one bipartisan measure in Congress.

Democrats on three House panels continue to meet privately to seek consensus on a single plan. Democrats on the House Ways and Means Committee said they were trying to decide whether to finance coverage of the uninsured with one broad-based tax, like the value-added tax, or a combination of smaller taxes.

The value-added tax, common in other countries, is collected in stages from each business that contributes to the production and sale of consumer goods. Economists say a 5 percent VAT could have raised $285 billion last year.

But a VAT could violate Mr. Obama’s campaign pledge not to raise taxes on households with incomes under $250,000 a year.