The defendant in the Angie Zapata murder trial appears likely to argue (based on comments during jury selection) that he did kill Zapata but only did so in the heat of passion, rather than intentionally and deliberately. A heat of passion defense is not grounds for an acquittal under the applicable criminal law.
The defense is likely making this limited case primarily because enough of the defendant's confession will come into evidence, and this confession is supported by enough physical evidence (e.g. the defendant was in possession of Zapata's car) to corroborate it, to make a more ambitious case unlikely to succeed.
An open request to the jury from the defense that it ignore the law, moreover, would probably produce a mistrial charged to the defense (and hence not subject to double jeopardy limitations), although the defense will likely do what it can to make a sympathic case that could move the jury to ignore the law without being expressly asked to do so.
Pre-trial proceedings indicate that the Defendant is a habitual offender and that the prosecution is not seeking the death penalty in the case. Thus, the jury may acquit (in what would amount to a jury nullification of the applicable law, but is not reviewable on appeal), convict of murder in the heat of passion (a 40 year to life sentence for a habitual offender) or convict of first degree murder (a life without possibility of parole sentence).
The defendant, Allen Andrade, is 32 years old, so he will be an old man when he leaves prison, if he ever leaves prison, unless the jury disregards the law. The trial is scheduled to begin tomorrow.
A key open qustion is whether Andrade will choose to testify. This would probably open the door to allowing the prosecution to let the jury know that Andrade is a career criminal, which makes him much less sympathetic the jury and less trustworthy. This could harm a jury nullification bid and a mere shorter sentence may be something that Andrade does not live to enjoy anyway. But, if Andrade testifies about the events in question, there will be no other eye witnesses who can question him, so it will be easier for him to argue his intent, something physical evidence can only suggest inferrentially. Testifying could also humanize Andrade who otherwise is just a scowling face and admitted killer at the defense table to the jury. I suspect that in this case, the pros of testifying will outweigh the risks for Andrade.