They're still working on the case, but have given up the search and rescue operation for now, said Lt. Chris Mealy of the Thurston County Sheriff's office.
"We're working on a bunch of different theories. We really haven't closed any possibilities yet," Mealy said. "We will find her."
It's still possible the 29-year-old mother and her son went into the water of Puget Sound, but if they did, Mealy said, they could be anywhere in the region because of the ferocity of the current.
Meanwhile, the boy's father has arrived in Washington to look for them.
Jay Carver arrived at Seattle-Tacoma International Airport from New York late Tuesday and said he planned to rent a car and drive to Olympia, where his former partner and their son were last seen Saturday night.
Carver told Seattle television stations he's frazzled and wants to get out in the woods and start looking for Smiley and their son.
Smiley was en route from her Kitsap County home to her stepfather's house in southwest Washington when she and her son vanished Saturday night. Silverdale is about 16 miles west of Seattle, across the Puget Sound.
The van Smiley drove was found Sunday, abandoned and partially submerged in water on a remote Puget Sound beach in the Olympia area.
Investigators were looking at phone records and talking to people who know Smiley or her son and those who may have met her as she drove through the back roads of Washington state on Saturday night.
Her fiance, Robb Simmons said Tuesday that Smiley is a recovering alcoholic who relapsed last week, KING-TV reported. But he said he doesn't believe the relapse played any role in her disappearance.
Mealy said Wednesday that Thurston County detectives were aware of Smiley's emotional state and her problems with alcohol.
He said Simmons is not a suspect.
Anyone with information on Smiley and her son's whereabouts should call Thurston County Crime Stoppers at 360-493-2222 or the Thurston County Sheriff's Office at 360-786-5500.
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