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“To say in 30 seconds what you would do with 18 percent of the economy, life and death for the American people, a topic I’ve worked on since 1974, about which I wrote a book called ‘Saving Lives and Saving Money’ in 2002, and for which I founded the Center for Health Transformation, is the perfect case of why I’m going to challenge the president to seven Lincoln-Douglas-style three-hour debates,” Mr. Gingrich said to cheers from the audience.

As the only medical professional in the GOP field and the strongest advocate for the free market, Mr. Paul focused on stronger doctor-patient relationships and ending government insurance programs in favor of health savings accounts.

He has his own ideas for Medicare. Instead of turning it into a voucher system, he wants to end it for those not yet enrolled. He also proposes keeping down the costs of medical-malpractice insurance not by capping awards, but through a tax credit for “negative outcomes” insurance to compensate patients for medical mistakes.

Rep. Michele Bachmann of Minnesota says insurers should be allowed to sell plans across state lines and has called for tax breaks for all medical-related expenses as well as tort reform. She also has supported reducing future Medicare benefits for Americans younger than 55 and allowing small businesses to band together through trade associations to purchase cheaper insurance. She voted for Mr. Ryan’s budget, but later said it could hurt seniors.

Back to the states

Other candidates have said less about exactly how they would improve health care, whether or not Mr. Obama’s law was repealed.

Mr. Perry proposes a gradual raise in the Medicare eligibility age, but his “cut, balance and grow” economic plan offers few other details. He told the debate moderator that seniors should be given more coverage options, and then touched on the health care topic tied most closely to his role as governor: Medicaid.

“You send it back to the states and let the states figure out how to make Medicaid work because, I’ll guarantee you, we will do it safely, we will do it appropriately, and we will save a ton of money,” he said.

Although he has supported tort reform, Mr. Perry’s record on health care mainly involves resisting government health care programs and their impact on Texas, which continues to log the highest uninsured rate of any state. He tried to opt his state out of Medicaid last year after repeatedly resisting the program’s rules. He has cited the 10th Amendment in his arguments that states should be able to opt out of Medicare and provide their own means of health care for the elderly.

He also threatened this year that he would veto a bill authorizing the state to begin setting up an insurance exchange, a requirement under the federal health care law.

Empowering patients

Former corporate CEO Herman Cain pointed to a health care plan championed by Rep. Tom Price, Georgia Republican and a physician, as his “starting point.” The Empowering Patients First Act preserves the system of employer-sponsored insurance, but includes tax breaks for purchasing insurance in the individual market, among other reforms.

As a business owner who bought coverage for his employees and as a survivor of cancer found in his colon and liver a few years ago, Mr. Cain brings a markedly different background to the field. “I am walking proof that we have the best health care system in the world,” he told reporters this month. “I was able to make some decision about my cancer treatment. That’s why I am alive today.”

The one unifying position all have, however, is a repeal of the Democrats’ moves. The position is sure to curry favor, at least in the primaries, as more Americans now say they are opposed to the law than in favor of it.

“I think that repealing the Affordable Care Act is just such a clear call and such a clear policy proposal that it’s almost standing in as a symbol on what candidates would do on health care,” said Elizabeth Rigby, a professor of public policy at George Washington University. “It’s such a generic position that it’s easy for people with many, many, many different priorities to agree to it.”