Shifting stances and a lack of clear standards from the governors of New York and New Jersey over their Ebola quarantine policy left critics and even some allies questioning on Monday whether the two men had fully worked through the details before they announced it.

In New York, local health officials said on Monday that they had not yet received any details of the three-day-old Ebola quarantine policy they are charged with enforcing.

In New Jersey, requests for such specifics were met with six sentences from a Friday news release.

An ongoing behind-the-scenes skirmish between the White House and state governors on how best to handle Ebola cases is becoming even more convoluted as several states announce they are following New York and New Jersey in ordering quarantines and other precautions that go well beyond federal guidelines -- and run contrary to Obama administration recommendations.

New Jersey Gov. Chris Christie called the Obama administration’s new guidelines for isolating those exposed to Ebola “incredibly confusing,” and defended the state’s stricter policy requiring quarantines for health-care workers exposed to the virus.

“We aren’t moving an inch,” Mr. Christie said during an interview on the “Today” show Tuesday morning. “Our policy hasn’t changed and it will not change.”