@Thomas,
What he tells the police is after the suspect has been read his Miranda rights.
If he agrees, there's nothing more the jury has to take into consideration about the suspect's lies. The judge's instruction to the jury is also pretty clear; if the defendant is caught in a lie, the jury is free to think everything that the suspect says is a lie.
Try to get around that with "beyond a reasonable doubt" - even in this case where Zimmerman's lies will probably determine his fate.
If the jury has a question about any of the evidence presented, and they must choose, they'll probably lean towards not trusting Zimmerman.
I would think.