A bailiff told a judge that Christopher Vasata was "medically unable" to appear in court, pushing the hearing to Wednesday at 9:30 a.m.
Vasata, 24, of Jupiter, was charged Monday with three counts of first-degree murder in the case.
Police said he was the gunshot victim found in the Paseos neighborhood the night of the slayings.
Vasata was rushed to hospital for gunshot wounds to his lower back/butt, Vasata had been recovering from his injuries.
In a police report released Tuesday, police say Vasata was found with a loaded handgun, a black glove and stray bullet. The bullet later matched those located at the house on Mohawk Street.
Police said they have been gathering evidence to charge Vasata in the shooting deaths of Sean Henry, 26, Brandi El-Salhy, 24, and 20-year-old Kelli Doherty.
The victims were found dead Feb. 5 in the backyard of the home on Mohawk Street.
Police said at a Monday evening news conference there still might be another shooter that was involved, and it remains an active investigation.
Charlie Vorpagel, the renter of the house where the homicide occurred, said three to four masked people opened fire on him and his guests. Vorpagel said Vasata had not been invited to his house and must therefore be a suspect.
At the hospital Vasata told police, after the shooting he had a spiritual moment and said, "Here I am, looking at heaven. I just killed three people and I'm looking at heaven."
Vasata later denied saying that to police. He is charged with three counts of first-degree murder, attempted first-degree murder and a convicted felon in possession of a firearm.
Anyone with information in the case is urged to contact the Jupiter Police Department at (561) 746-6201, or Crime Stoppers of Palm Beach County at (800) 458-TIPS (8477).