The first was Dr. Alieta Eck, also a physician in private practice, who is running for the Republican nomination in New Jersey, which will hold a special election this fall to fill the Senate seat left vacant by the death of Frank Lautenberg. Like Bosworth, Eck has no political experience but was motivated to run for public office to repeal Obamacare, which she called a "disaster waiting to happen."
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"If I can make a difference in Washington—I hope to get Obamacare repealed—then I think I will be doing a great service to the American people," Eck told CNBC in a phone interview. She added, she is opposed to Obamacare because she does not approve of government mandates and increased taxes.
While Bosworth and Eck do feel the federal government should continue to work with state and local health departments to safeguard communities from public health threats, they argue Obamacare is overreaching, costly and ineffective.
Though the Obama administration recently decided to delay the mandate for larger employers to offer health coverage, Bosworth told CNBC she doesn't think any business—large or small—needs to offer health insurance, much less allow the government to require it.
"The federal government should never be controlling the choices of our health care," Bosworth said. "If you want people to make their best decisions for their health care, they not only need to be engaged in the decisions and be a part of this process, but it can't be served up in a way that's one-size-fits-all."
Under Obamacare's individual mandate, the uninsured will be able to purchase health insurance on federal- and state-run health exchanges beginning Oct. 1. The individual mandate is key to the law's mission of covering more than 30 million uninsured. The Obama administration has argued it is only by requiring healthy people to purchase policies that they can help pay for reforms, including a provision that individuals with pre-existing medical conditions cannot be refused coverage.
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Bosworth said she would seek to replace Obamacare with legislation that improves and enhances safeguards to public health, but would remove any individual or employer mandates. She plans to unveil her full plans in the coming weeks.
Eck, on the other hand, said she will not replace Obamacare with any reforms. To care for the health needs of the poor, she suggests getting every medical doctor to volunteer four hours a week at a health clinic for the needy.
Doctors as problem-solvers
Both Bosworth and Eck think their years of medical training and experience perfectly qualify them for the job on Capitol Hill. Doctors are basically problem-solvers, Eck said.
"We look at problems, we take down all the symptoms, we examine the patient and then we prescribe ways to make them feel better or get better, and I feel like we can translate that right into the government," she said. "As we look at the problems that out there that our nation is facing, a lot of the solutions that the politicians are coming up with don't make sense, and I'd like to be able to weigh in on them [and] get back more to the Constitution."
Three medical doctors currently serve in the Senate; all are Republicans opposed to Obamacare: Rand Paul of Kentucky, Tom Coburn of Oklahoma and John Barrasso of Wyoming.