"I need a voice," Martinez said.
Eck, a Republican who has never before sought or held public office, says people like Martinez inspired her to run for the seat vacated when Democratic U.S. Sen. Frank R. Lautenberg died in June.
"That lady is Exhibit A," Eck said in an interview this week at the clinic.
Of course, if Martinez cannot afford insurance, she could be eligible for Medicaid or, soon, under the new health law, a subsidy to buy insurance.
But Eck says doctors often don't accept Medicaid, the government-run health program for low-income individuals, limiting patient choice and flooding emergency rooms with people seeking noncritical care.
Eck's clinic, open 12 hours a week, is housed in a nondescript trailer off a two-lane highway. She volunteers four hours a week and also runs a private internal-medicine practice in Piscataway Township, Middlesex County.
Most of the equipment and drugs at the clinic are donated by companies such as GlaxoSmithKline and Merck.
Eck said her experience at the clinic - and her belief that the Patient Protection and Affordable Care Act, or "Obamacare," will fail - pushed her to run for Senate. The clinic, she says, is a microcosm of how health care should be provided for the poor.
Eck opened the clinic in 2003 with her physician husband, John, after reading Marvin Olasky's The Tragedy of American Compassion, which criticizes welfare.
"I realized there's a better alternative" to government aid, said Eck. "The Bible teaches that you help those who are in need. So if we could energize the churches and help them to start clinics like this, we could do without taking from hardworking taxpayers."
On the campaign trail, Eck has blasted Obamacare, calling "a stay of execution" the administration's recent decision to delay a mandate in the law that employers with 50 or more workers provide them with insurance.
"Experts are trying to figure out how to make a terrible law work," she told members of the Independence Hall Tea Party on July 4. Employers, Eck said, are cutting workers' hours because they don't want to pay for health insurance or pay a fine.
Meeting on Wednesday with the Inquirer Editorial Board, she expressed views on a range of other issues, hewing to the far right of her party on most, including questioning climate change. On abortion, however, Eck said while she is "pro-life," a federal overhaul of Roe v. Wade would be "impossible to implement."
Eck supports state legislation introduced in October by State Sens. Robert W. Singer (R., Ocean) and Brian P. Stack (D., Hudson) that would provide civil liability protection to medical professionals who volunteer four hours a week at a free clinic. The bill stalled in committee, and Singer said he planned to reintroduce it next year.
"If this law could get passed in New Jersey and I became a U.S. senator, I'd be able to champion this cause across the country," she said at her clinic. "And it's true entitlement reform."
Eck's critique of government-provided health care predates the passage of the Affordable Care Act in 2010. In 2004, she testified before Congress' Joint Economic Committee that health-maintenance organizations turn doctors into their "servants."
In prepared remarks, she quoted a passage from Ayn Rand's 1957 novel, Atlas Shrugged - a fierce critique of government coercion - about a doctor who quit medicine after it came under state control.
"The only real insurance is the kindness of our families, our churches, and our communities," Eck said.
She said her views closely aligned with libertarian Republican Sen. Rand Paul of Kentucky, a fellow member of the conservative Association of American Physicians and Surgeons. Eck was president of the group in 2012.
At a 2011 hearing before the Health, Education, Labor, and Pensions subcommittee, Eck and Paul sparred with U.S. Sen. Bernie Sanders (Ind., Vt.) over whether people have a right to health care.
Eck said, "If health care is a right, so is food care, and shelter care, and clothing care. . . . Yet we don't expect the government to provide food, clothing, and housing to everybody."
In 1997, Eck, her husband, and their five children eschewed commercial health insurance for Medi-Share, a Christian medical cost-sharing program.
Her family pays $408 a month to participate, as well as an annual family portion equivalent to a $10,000 deductible. Unlike Obamacare, Medi-Share does not cover preexisting conditions or things like abortion. The group decides what it will cover.
It "goes with the biblical principle of bearing one another's burdens," Eck said.
Eck faces long odds in the Aug. 13 primary. A July 9 Quinnipiac University poll showed her opponent, former Bogota Mayor Steve Lonegan, leading by 57 points. Newark Mayor Cory Booker is the favorite on the Democratic side, leading Assembly Speaker Sheila Oliver and U.S. Reps. Frank Pallone and Rush Holt by about 40 points.
As of June 30, Eck had raised $29,000 compared with Lonegan's $193,000.
With more than a hint of frustration, Eck said Lonegan is "trying to ignore me. He's not even addressing that he has a primary candidate."
But she believes the expected low turnout for an August primary and October special election could render polls meaningless as she tries to build her profile. Referring to the freshman Republican senator from Texas, Eck said, "Ted Cruz says he had 1 percent his first poll."
Friday: Democrat Rush Holt.
Alieta R. Eck
Piscataway Township, Middlesex County
St. Louis University School of Medicine
Family: Married, five children
Key cause: Anti-Obamacare
Contact Andrew Seidman at 856-779-3846 or firstname.lastname@example.org, or follow on Twitter @AndrewSeidman.
Inquirer staff writer Jonathan Tamari contributed to this article.