"We are optimistic, but it's wait-and-see," said Pamela Paugh, sister of JonBenet's mother Patsy Ramsey, outside her family's Roswell, Ga. home. "We've been patient for nine and a half years; what's a few more months?"
Karr remained jailed in Thailand on Friday, one day after his public proclamation there that he was with JonBenet when she was killed in Boulder, Colo., in 1996. He is due back in the U.S. on Sunday.
A Thai police general said, "The tickets for 41-year-old John Mark Karr's departure are ready."
Karr said Thursday that he wasn't innocent in the case, but questions have been raised about some of his claims.
Paugh, who has acted as her family's spokeswoman since the arrest, said the family has its own concerns about Karr's statements but remains confident in the work of Boulder County District Attorney Mary Lacy and other investigators.
"She would never do something (haphazardly) when she knows the world's eyes are on her," Paugh said of Lacy. "She's not going to just go out there willy-nilly and pick up some nut case."
CBS News legal analyst Andrew Cohen, who has followed the Ramsey case extensively, agrees.
"If they don't have anything, they become laughingstocks of all time in the law enforcement profession, and I'm simply unwilling to believe that," Cohen says of the Boulder DA's office.
Paugh said she's spoken with JonBenet's father, John Ramsey, but did not know where he currently is. She said he's upbeat about the arrest, but not yet ready to speak publicly.
"It's a very touchy thing right now," Paugh said. "All this is bringing up some very hurtful and terrible memories, even though it's a good thing; he just needs some alone time."
Meanwhile, police in the town just north of Atlanta where Patsy Ramsey spent the final months of her life, declined to comment Friday on whether they had set up a ruse to trap e-mails or letters that Karr tried to send Ramsey.
The family's attorney, Lin Wood, in Atlanta said Patsy Ramsey never received the correspondence because police or someone else set up an address. "He thought that he was corresponding with Patsy, but he wasn't," Wood told The Associated Press.
A spokesman for the Roswell Police Department, which helped to identify and locate Karr, declined to say Friday whether his agency conducted the correspondence ruse.
"We're not commenting on any part of the investigation," Sgt. James McGee said.
Authorities asked Ramsey in late May — a month before she died of cancer — whether she would be willing to meet with Karr, Wood said.
Ramsey said she would meet with Karr if it would advance the investigation into her daughter's slaying, but the meeting never took place because authorities did not get back to her before she died in June, Wood said.
For most of Friday, speculation swirled around e-mails Karr sent regarding Ramsey's death. The day before Christmas Eve 2005,sent an e-mail to University of Colorado professor Michael Tracey. It was one of a disturbing between Tracey and a person investigators believe to be Karr.
A source close to the investigation told CBS News the reason investigators moved in on Karr was because of details in these emails about the Ramsey house that had not been made public, reports CBS News correspondent Kelly Cobiella.
Correspondence obtained by the Rocky Mountain News included one message in which the professor was asked to visit JonBenet's home in Boulder to read aloud an ode called "JonBenet, My Love."
Tracey once worked for CBS News as a consultant on the Ramsey case.
"JonBenet, my love, my life. I love you and shall forever love you. I pray that you can hear my voice calling out to you from my darkness, this darkness that now separates us," read one of the e-mails, which the newspaper said Friday it obtained from a source close to the investigation.
In other e-mails, Karr said he was under federal investigation for "child murder and child molestation" in four states.
"I don't know that he's guilty," said Tracey. "Obviously, I went to the district attorney for a reason, but let him have his day in court and let JonBenet have her day in court and let's see how it plays out."