The Supreme Court as well as others have ruled repeatedly that mandatory death sentences are unconstitutional. I could easily just vote against the death penalty in the sentencing phase, as it must be unanimous to impose it. There's also what CARL said. So the scenario could never happen.
In addition to what Carl says, the SC has also seen fit to declare it unconstitutional, in death penalty cases only, to take sentencing out of the jury's hands. It is therefore entirely unproblematic to agree to a guilty verdict but hold out for life without parole. (Yeah, so it's a hypothetical. I'm dealing with it.)
Let's not assume that the scenario takes place in the United States. 
Correct me if I'm wrong, but I don't think there is another country where both these barbarisms, jury trials AND the death penalty, still survive.
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