President Obama traveled to Chicago on Monday to try to win over a critical and wary group of stakeholders in his health-care reform effort -- the nation’s doctors.

Ahead of his address to the annual meeting of the American Medical Association, the President laid out additional budget cuts he said will help pay for health-care reform, which is expected to cost $1 trillion or more over 10 years and is intended partially to provide health-insurance coverage to the more than 46 million Americans who don’t currently have it.

In his weekly radio address on Saturday, the President spelled out an additional $313 billion in savings that he said “will rein in unnecessary spending and increase efficiency and the quality of care.”

Combined with another $635 billion in spending cuts and tax increases the President announced in his budget outline in February, the changes would total $950 billion over a decade.

The President stressed to the AMA that the U.S. spends too much for health care and gets too little in return, and reiterated the core principle of the reform effort: that if you like the health care you have, you can keep it, and that his focus will be on fixing what's broken and building on what works.

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The President asserted that the U.S. is spending too much money on treatments that don't make Americans any healthier, and that our system equates more expensive care with better care, and laid out his vision for a system that replicates best practices, incentivizes excellence, and closes cost disparities. He asked for medical professionals' help in getting the job done.

The President was expected to tell doctors he'd work toward something they've long wanted: tort reform. Senior White Officials said that President Obama and Chief of Staff Rahm Emanuel have told lawmakers in private meeting they would accept some malpractice liability reforms in order to win support for health-care reform from doctors and Senate Republicans.

Medical malpractice is one issue where the AMA did not want to lose negotiating clout and figured prominently in its decision not to close off all consideration of a health care "public option." None of the bills currently circulating in Congress contain medical liability reforms, which Democrats have traditionally opposed.

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In his radio address, the President singled out doctors, often the key decision makers in health treatments, as participants who can help reduce costs.

“These savings will come from common-sense changes,” the President said. “For example -- if more Americans are insured, we can cut payments that help hospitals treat patients without health insurance.  If the drug makers pay their fair share, we can cut government spending on prescription drugs. And if doctors have incentives to provide the best care instead of more care, we can help Americans avoid the unnecessary hospital stays, treatments, and tests that drive up costs.”

About half the February savings would come from higher taxes on wealthier Americans -- $326 billion. The rest -- $309 billion -- would come from reductions in Medicare spending and other expenses. In the new round of cuts announced Saturday, most would come from squeezing Medicare and Medicaid even more.

Doctors said this weekend ahead of the President’s speech that they are particularly anxious about the President’s support for a possible public health-insurance program that would compete with private health-insurance companies.

The President and reform supporters have made it clear that part of the idea behind a public health-insurance company -- essentially Medicare for everyone, not just senior citizens -- is to help keep costs down. And that could mean lower compensation for doctors, whether they are paid by the federal plan or by private insurance firms forced to cut their costs because of competition from it.

“If the private insurance companies have to compete with a public option, it'll keep them honest and it'll help keep their prices down,” the President said in a town-hall meeting on health care in Wisconsin last week.

In a letter to the editor published Saturday in the New York Times, AMA president Nancy Nielsen wrote that the organization “is committed to health reform that covers the uninsured this year. Every American deserves affordable, high-quality health care, and the AMA is calling for reforms that build on what works and fixes what’s broken."

But she added, “A government-run health care plan is certainly not the only option on the table, and there are alternatives we are actively considering.”

Congress dives into health-care reform this week, with leaders planning to have a bill approved by each chamber by the August recess and final negotiations in September.

Some key developments slated for the week:

• On Monday, the Congressional Budget Office -- the official budget scorekeeper for Congress -- will release its first estimate of what major health care reform could cost. It has been looking at the reform bill crafted by Sen. Ted Kennedy (D-Mass.), a key player in the process as the chairman of the Senate Health, Education, Labor and Pensions Committee. His bill is ambitious, proposing to require businesses and individuals to purchase medical coverage; to bar insurance companies from refusing to cover anyone because of preexisting conditions, and to provide generous federal subsidies to families purchasing buying coverage. Analysts expect the cost could come in at $1.5 trillion or more over 10 years.
• Republicans have opposed key parts of Kennedy’s and the President’s proposals, in particular a federal health insurance plan. On Monday, the second-ranking Senate Republican, minority whip Sen. Jon Kyl (R-Ariz.), will hold a news conference to explain an alternative healthcare reform bill he will introduce on Tuesday.
• On Tuesday, the Senate Health, Education, Labor and Pensions Committee is scheduled to begin marking up the Kennedy bill. 
• On Wednesday, the Senate Finance Committee, which has jurisdiction over how a comprehensive healthcare bill would be paid for, plans to release a draft bill for comment. 

Handicapping the unfolding debate, Washington policy analyst Tony Brush of TBrush Company said in his weekly client letter that while reform is moving forward, “there’s no broad consensus about its contents; no one knows what it will cost…With some estimates for the 10-year cost of health-care reform pegged at $1 trillion or higher, $400 billion to $600 billion over 10 years may be a lot to wring from efficiencies while expanding coverage to some 46 million people.”

“Moreover,” Brush wrote, “there are indications that the legislative effort could bog down if most Republicans and groups like the fiscally conservative Blue Dog Democrats [in the House] doubt that health-care reform legislation will curb costs while maintaining current levels of care.”

Brush also told clients that among tax proposals that policymakers could approve to help raise funds to pay for reform, “the proposal with the most traction appears to be one to cap the employer exclusion on health benefits at the Federal Employees Health Benefit Plan level for single filers with adjusted gross incomes above $100,000, and joint filers with adjusted gross incomes above $200,000, indexed to the per capita medical cost growth index for years after 2010. A second proposal being discussed would repeal the itemized deduction for medical expenditures above 7.5% of adjusted gross income. Together, these provisions would raise $343 billion over 10 years.”

“The one financing option that appears to be off the table at the present time is deficit financing,” Brush added, especially in light of recent warnings from Federal Reserve Chairman Ben Bernanke about the impact of rising budget deficits on the nation’s long term fiscal health.

--FOX News's Major Garrett contributed to this article.