Or there is a point where your attorneys tell you that they have you red-handed with no expectation of a legitimate defense.
No lawyer would ever say that for a few reasons. The first is that the prosecution still needs to follow "due process" which takes forever just to get to the original conviction. After which the prosecution gets to spend the rest of their lives responding to the appeals. Who pays for the legal defense service and the prosecution? The State. The sum total is that you can trade in a guilty plea for a lighter sentence.
From a strategic stand point one would never plead guilty, however like I mention above, after watching every video they have of you (and with the FBI in on the operation from the front and with agents on the inside we can guess that the amount of footage that they actually have is days worth) most people freak out. The defendant tells the attorney "it's easy for you to walk out there and give some B&$# S%$# reason why I am technically innocent, however I am going to look like a total freak standing on TV watching the full length of footage together with the entire world and still claiming my innocence. That my friends is not an easy task.
At that point in time a defendant also just hopes that the judge will be lenient because he rolled over.
I am not going to go into the rest of the reasons that no lawyer would ever say that, because it would bore both you and me to death.