Lisa Irwin's mother Deborah Bradley is not keeping a low profile during the investigation of her daughter's disappearance, despite her own admittance that she believes police suspect her involvement. (Kansas City police have denied any intention to arrest Bradley, and have not named any suspects).

After Bradley admitted that she was drinking the night baby Lisa disappeared, and changed the original timeline she gave investigators, Bradley and Lisa's father Jeremy Irwin have retained high-profile New York lawyer Joe Tacopina, who previously represented Michael Jackson in his molestation trial, and Jordan van der Sloot, who remains in prison on charges connected to the 2005 disappearance of Natalee Holloway.

In my mind, there is no question they had nothing to do with the disappearance of their little girl, Tacopina said in a press conference for local media. I'm optimistic and confident at the end of the day the truth will come out and speculation will be put to rest.

Bradley has said repeatedly that police have treated her as a suspect, and she claims they told her she failed a lie detector test. (Kansas City Police have not confirmed or denied the lie detector story).

Police have to start with the mother and father, they have to look at that but don't come to any conclusions because there's no other answers, Tacopina told KCTV in Kansas City. They have nothing to hide. I don't recall anyone being so open and honest under such an umbrella of suspicion.

Baby Lisa Irwin disappeared two weeks ago, and was reported missing by her parents on Tuesday, Oct. 4, after Jeremy Irwin discovered the baby was not in her crib when he arrived home from work early that morning. An Amber Alert was issued later that day.

Surveillance footage had put Bradley in a local liquor store buying wine the day before baby Lisa was reported missing. Bradley was accompanied by a man who was later identified as her brother. On Sunday, Bradley told Fox News she had several glasses of wine with a neighbor later that night.

Bradley told Alexander that she consumed enough to be drunk.

When asked if she felt she might have been incapacitated enough to harm Lisa, Bradley insisted not.

No, no, no,'' she told Alexander. If I thought there was a chance, I'd say it. I don't think that alcohol changes a person enough to do something like that.''

Since Lisa vanished, Bradley had maintained she last saw her daughter at around 10:30 p.m. CDT on Monday, Oct. 3. But now Bradley says she last saw her at around 6:40 p.m.

Bradley told Fox host Megyn Kelly of America Live that she was not sure one way or another if she checked on baby Lisa after putting her to bed. Most of the time, I check on her, Bradley told Kelly, adding that she was sure she checked on her older sons. I'm assuming I went and checked on her too.

Bradley reportedly told Kelly she spent the evening of Oct. 3 drinking wine on her porch with a neighbor. I don't see the problem with me having my grown-up time...There's nothing wrong with me doing what I want to do after dark.

It's unclear why Bradley came forward with this revision two weeks into the investigation.

(Being drunk) would explain why she didn't hear the baby monitor, she didn't hear the dog barking,'' former district attorney Jeanine Pirro told Ann Curry on Today. People were believing her because her story was consistent. Now she comes out with, 'The last time I saw my baby was at 6:40 and by the way, I was drunk.' This isn't the kind of thing that you want to bring out after the fact when time is essential here.''

Tacopina critized Kansas City police for their treatment of his client in the immediate wake of baby Lisa's disappearance.

Some of the local police officers in this case have conducted themselves in a way that to me is baffling. For instance, within hours of their reporting this baby missing, which was instantaneously, where Deborah is trembling, one of the interrogators, I'll call them, actually accused of her of murdering her baby without a stitch of proof, Tacopina told Good Morning America.  Imagine for a second, assume, that this baby was kidnapped or taken, and this mother who's in terror is being accused, without any evidence, by the person who's supposed to be helping her find her baby of committing murder.

Tacopina has refused to disclose who is paying him. It is not clear if it is the same anonymous benefactor who posted a $100,000 reward for information leading to Lisa's safe return or the arrest of her kidnapper.

Watch Tacopina discuss missing baby Lisa Irwin's case on Good Morning America: