Earlier in the day, as Utah families and visitors gathered on Salt Lake City's Main Street for an enjoyable morning of watching the parade, Lori Hacking's parents continued to plead for help in finding their missing daughter.

"She's still out there somewhere. We need your help to find her," her mother, Thelma Soares, said tearfully. "Please help us find her one way or another."

The Hacking and Soares families stood together at a press conference Saturday morning. They expressed support for Mark Hacking, as they have each day this week. But behind the scenes there was apparently a rift developing.

Herald Soares, Lori's father, told Fox News Network Saturday that if Mark did have something to do with his daughter's disappearance, he wanted him to come clean.

"To a certain degree, I have to draw the line; I want my daughter back," he told the news network. "I want him to retrieve the body so we can give her a proper burial."

Lori Hacking was last seen sometime Sunday night after going to a party with her husband. She reportedly went jogging in Memory Grove Monday between 5:30 and 6 a.m. Monday. Police were notified of her disappearance at 10:49 a.m.

Mark Hacking has remained hospitalized since early Tuesday, after he was found by police naked at the Chase Suite Hotel, 765 E. 400 South, allegedly creating a disturbance.

Douglas and Janet Hacking, Mark's parents, were not at Saturday morning's press conference. Their oldest son, Lance, said they were at the hospital visiting Mark and might have been delayed by parade traffic.

The time line

Some of the biggest questions being raised in the case concern the time line of alleged events.

During Mark Hacking's only public comments since his wife disappeared and before he was admitted to the hospital, he said he tried contacting her at work Monday at 10 a.m. But Hacking also went to Bradley's Sleep Etc. about 10 a.m. and purchased the new mattress at 10:23 a.m. Between 10:30 a.m. and 10:35 a.m. he left the store parking lot with the new mattress tied to the roof of his car.

Police were called at 10:49 a.m. When they arrived at Memory Grove, Mark Hacking had reportedly already twice jogged a three-mile route in the canyon looking for Lori. Neighbors did not report seeing a car with a mattress.

"We have a lot of questions about that time line," Baird said Saturday. "We know things about that time line we're not going to divulge."

Police also were remaining tight lipped about how many items they have sent away to the crime lab for analysis.

Local television station Fox 13 showed video of a box spring being removed from the Hackings' apartment Monday with an obvious red stain on the corner.