Police said it is possible that Taylor lives in either Jackson or Hillsdale, Mich., but they are not sure the woman even exists.
The FBI and Michigan State Police are also involved in the search.
Neighbors of the Skelton family say they're shocked that the boys are missing.
"They lived across the street from me, I used to watch them playing outside, being boys and having fun," neighbor Jody Pummell said.
Family friend Shelly Meyers said, " A lot of people didn't sleep the last couple of nights, that's for sure."
Searcher Steve Clegg said, "We haven't had anything remotely close to this happen and now to have something this happen, yeah, it hits home."
Alexander Skelton is 3-foot-9, 45 pounds and has brown eyes, brown hair and a scar on his chin. Tanner Skelton is 3-foot-6 with blue eyes and blonde hair. Andrew Skelton 4 feet tall, with brown hair and brown eyes.
Morenci police asked that anyone with any information about the boys' whereabouts or who might have seen John Skelton with them any time after Thursday, contact them at (517) 263-0524.
ABC News' Dean Schabner contributed to this report.