For those who don't know how PDO's usually work, while he was assigned one today it's almost always not the same one that represents you at trial.
As soon as any defendant fills out the needed paperwork that shows they are indignant and cannot afford an attorney of their own, the judge must assign them someone from the PDO. Failure to do so would be a major violation of a core Miranda right.
The PDO office usually has representatives in the courtroom or nearby in criminal cases so as to adhere to that right. The one that he was assigned today is likely just there for now to advise him on court procedural matters and so he can't claim later he wasn't afforded an attorney. If I recall, many PDO's have a similar structure to normal law firms in they have clerks, associates and trial lawyers.
From here on out, he has the right to be professionally advised on any court proceedings so while it's unlikely the woman who talked to him today after the hearing will defend him at trial, she is making sure that he understands all procedural matters before him leading up to that.
It's also possible - unlikely but possible - that a private law firm will take up his case pro bono or at a reduced rate. Law firms do this sometimes in high profile cases as essentially publicity builders. Chad & Jennifer Freese did something similar to defend Mollie Tibbett's killer because he in no way could pay for their services.
In the end it's highly unlikely to matter because from what we've even seen there is a mountain of physical and video evidence that places him at the scene of the crime at the same time as Eliza and his DNA at the scene and presumably on her body. That will leave any attorney - regardless of skill or competence level - with very few options to have him avoid anything but the max sentence and at this point, when the case is so strong, that's what you typically are shooting for as a defense lawyer.
Acquittal and/or 'walking free' is not an option. It's not going to happen. Zero chance of this. He will spend an incredibly long time in prison - if not the rest of his life.