Washington (CNN) -- Gov. Chris Christie's office said Monday that the nurse quarantined at a New Jersey hospital is being allowed to transfer to Maine, the latest development in a medical and political saga regarding possible cases of Ebola in the U.S., and how politicians in charge are responding.

A battle of words broke out during the weekend between Kaci Hickox, who returned home from Ebola-ravaged West Africa only to be ordered into quarantine, and the Republican governor. The nurse told CNN that her "basic human rights have been violated" and that Christie himself was responsible.

Hickox will be transported by a private carrier, "not via mass transit or commercial aircraft," read the statement, which was blasted out by Christie's office.

Gov. Paul LePage said in a statement Maine will work with Hickox "to establish an in-home quarantine protocol to ensure there is no direct contact with other Mainers until the period for potential infection has passed."

Steven Hyman, an attorney for Hickox, told CNN's Alexandra Field her first priority is to get out of the hospital and back to a normal life.

Hyman argued "there is a legal basis to challenge" the New Jersey policy, but "whether she wants to do it remains to be seen."

While in Florida campaigning for Republican Gov. Rick Scott, Christie stood by New Jersey's quarantine policy.

"I know she didn't want to be there. No one ever wants to be in the hospital, I suspect, and so I understand that," he told reporters. "But the fact is I have a much greater, bigger responsibility to the people and the public, and so I think when she has time to reflect she will understand that as well."

Hickox was the first medical professional to be quarantined in New Jersey immediately upon returning to the United States from West Africa, where she had worked in treating Ebola patients.

She lashed out at Christie during the weekend for giving her a diagnosis of sorts as "obviously ill."

"First of all, I don't think he's a doctor; secondly, he's never laid eyes on me; and thirdly, I've been asymptomatic since I've been here," Hickox told CNN's Candy Crowley in a phone interview Sunday.

"There always needs to be a balance, because I also want to be treated with compassion and humanity," Hickox said on CNN's "State of the Union" by phone from her hospital isolation. "I don't feel like I have been treated that way in the past three days."

Mandatory quarantines: Now what?

In an off-camera interview with CNN Senior Medical Correspondent Elizabeth Cohen, Hickox added, "I am not, as he said 'obviously ill.' I am completely healthy and with no symptoms. And if he knew anything about Ebola he would know that asymptomatic people are not infectious."

The White House seemed to agree with Hickox's sentiment that Christie doesn't have the medical authority to impose regulations that trump federal guidelines on handling Ebola patients.

A senior administration official told CNN on Sunday that the White House informed Christie and New York Gov. Andrew Cuomo -- who also ordered quarantine for people returning to his state from West Africa -- along with other state officials that it "has concerns with the unintended consequences of policies that are not grounded in science may have on efforts to combat Ebola at its source in West Africa."

Talking to reporters Saturday, Christie said he was "sorry if in any way she (Hickox) was inconvenienced, but inconvenience that could occur from having folks that are symptomatic and ill out amongst the public is a much, much greater concern of mine."

He added, "I hope she recovers quickly."

Cuomo elaborated on the New York position on Sunday, saying while the 21-day quarantine would remain mandatory for those coming in from Ebola regions after contact with infected persons, those who are symptom-free themselves will be taken to their homes, to wait out the quarantine period there. Health of those persons will be monitored by twice-a-day checks.

Nurse describes Ebola quarantine ordeal

"It's a home quarantine but it is a mandatory quarantine," Cuomo said.

Those coming from affected areas but having had no contact with infected people "will be monitored on a less rigorous basis."

And Cuomo added that if employers don't pay quarantined workers for the time they are absent while under quarantine, "the government will."

Meanwhile, New York Mayor Bill de Blasio -- with an Ebola-infected doctor undergoing treatment in his city -- took the New Jersey nurse's side Sunday.

At a news conference, de Blasio commented briefly on Hickox's case, saying that "what happened to her was inappropriate."

"This hero was treated with disrespect and was not given a clear direction," he said. "We owe her better than that, and all the people who do this work, better than that."

Christie's office put out its own statement Sunday night, saying the state was not changing its quarantine protocol. The statement added, "The protocol is clear that a New Jersey resident with no symptoms, but who has come into contact with someone with Ebola, such as a health care provider, would be subject to a mandatory quarantine order and quarantined at home. Non-residents would be transported to their homes if feasible and, if not, quarantined in New Jersey."

Neither governor explained how a home quarantine would work if family members were also in the home, or how a home quarantine would or could be enforced if the quarantined person chose to leave the house.

For Hickox, after being tested for a fever using a forehead thermometer, it was determined at Newark airport on Friday that she had a fever, and thus was subject to the mandatory health care worker quarantine. But Hickox said the result was "an instrument error."

"They were using a forehead scanner, and I was distressed and a little bit upset and so my cheeks were flushed," Hickox explained to CNN's Crowley.

"And I believe that there is some evidence that machine is not very accurate in these kinds of situations. So when I arrived in the isolation unit they took my temperature orally and it was normal," said Hickox, who also said that her temperature continued to remain normal following the oral test.

Christie, along with New York's Cuomo and Chicago Mayor Rahm Emanuel, said that the mandated quarantine is intended to protect public health, citing evidence that health care workers traveling from West Africa pose the greatest Ebola threat to their constituencies.

Quarantine measures were instituted by the officials in response to a returned health care worker who tested positive for the virus last week, after having been out and about in New York City public spaces.

That volunteer -- Dr. Craig Spencer -- was in serious but stable condition at a New York hospital on Sunday.

Christie -- who embraces his reputation as a straight-talker -- candidly defended his decision to impose the mandatory quarantine for health care workers, saying he had "no second thoughts."

"I believe that folks who want to take that step and are willing to volunteer also understand that it's in their interest and the public health interest to have a 21-day (quarantine) period thereafter if they've been directly exposed to people with the virus," Christie said on Fox News Sunday.

"I don't believe when you're dealing with something as serious as this that we can count on a voluntary system," he said. "This is government's job. If anything else, the government's job is to protect safety and health of our citizens."

Obama met Sunday with his Ebola response team, and a White House statement afterward appeared to refer to the quarantine issue. In the meeting Obama "underscored that the steps we take must be guided by the best medical science, as informed by our most knowledgeable public health experts," the statement said.

"He also emphasized that these measures must recognize that health care workers are an indispensable element of our effort to lead the international community to contain and ultimately end this outbreak at its source, and should be crafted so as not to unnecessarily discourage those workers from serving," the statement added.

That echoed remarks by Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases at the National Institutes of Health, who appeared on Sunday TV news talk shows arguing that imposing mandatory quarantines could have "unintended consequences."

On "State of the Union" Fauci told Crowley that putting "everyone in the same category" would result in "people not wanting to go over there (to West Africa)."

"You want to continue to make the safety of the American public paramount but it is critically important that you do that based on scientific evidence and data," he added.

And U.S. Ambassador to the United Nations Samantha Power spoke in the direction.

"We need to find a way when they (health care workers) come home that they are treated like conquering heroes and not stigmatized for the tremendous work that they've done, " Power said in an interview with NBC News before she left to visit Ebola-affected nations.

CNN's Kevin Liptak, Jim Acosta, NuNu Japaridze, Ashley Killough and Leslie Holland contributed to this report.