When President Obama brought his campaign to retool the U.S. health care system to the American Medical Association, his pitch wasn’t just directed at the more than 2,000 AMA members assembled in a Chicago hotel for the annual meeting of the influential doctors lobby.

Obama was simultaneously speaking to a broader segment of voters that polling indicates is still ambivalent about his plan to extend medical coverage to all Americans and put the health system under greater government control.

Though many Americans are frustrated with delays and inefficiencies in the health delivery system, Democratic polling suggests that as many as three-quarters of adults are generally satisfied with their insurance plans. Many of those individuals are risk-adverse and convinced that changes on the order of what Obama is talking about will ultimately cost them more.

A Rasmussen Report poll released Monday found that Americans are evenly split over the idea of creating a government-run insurance plan to compete with private health plans, as Obama has proposed. Only 32 percent of respondents believe that the addition of a public sector insurance option would reduce the cost of health care.

To address these negative perceptions, Obama used the speech to issue a three-pronged message. He stressed that his plan will reduce costs for individuals, expand coverage choices and at the same time, curb medical inflation that he says is threatening to bankrupt the economy.

Obama said critics who contend he is intent on engineering a government-run health system aren’t telling the truth. And to tamp down concerns he is quick to embrace expensive solutions to society’s problems, Obama elaborated on a series of cost-saving measures his administration identified that would deliver nearly $950 billion of savings that could be applied toward an overhaul.

The details of an overhaul plan will begin to emerge in coming days, when the Senate Finance Committee releases a draft in anticipation of a markup beginning June 23.

“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,” Obama told the AMA members on Monday. “So to say it as plainly as I can, health care is the single most important thing we can do for America’s long-term fiscal health. That is a fact.”

To punctuate his pitch, Obama dangled a potential sweetener for the group. He indicated he’s ready to incorporate measures to discourage medical malpractice lawsuits into an overhaul package. Obama echoed what many doctors and their supporters in Congress have long contended: that the fear of litigation is prompting physicians to engage in “defensive medicine,” by ordering an excessive number of tests and taking other steps to insulate themselves from potential suits.

“I recognize that it will be hard to make some of these changes if doctors feel like they’re constantly looking over their shoulders for fear of lawsuits,” Obama said. “I want to work with the AMA so we can scale back the excessive defensive medicine that reinforces our current system, and shift to a system where we are providing better care, simply — rather than simply more treatment.”

AMA support could be essential to firming up congressional support for Obama’s plan, because the group’s members reside in virtually every congressional district and are capable of applying significant pressure to their elected officials.

The AMA, which was founded in 1847 and has portrayed itself the “voice of medicine,” played a significant role supporting former President Clinton’s proposed “Patients’ Bill of Rights” in 1998 and George W. Bush ’s efforts to cap jury payouts in medical malpractice suits.

Republican majorities in Congress on eight separate occasions passed House bills to limit medical malpractice liability awards. But supporters repeatedly were unable to win enough support to get a vote in the Senate.