Under South Carolina law, 24 hours must lapse before jurors in a death-penalty case can be presented with new evidence as they decide the punishment.
The panel of nine men and three women deliberated for 2 1/2 hours Saturday before finding Smith, 23, guilty of first-degree murder for letting her car roll into a lake with her sons strapped in their car seats.
On Monday prosecutors are expected to detail aggravating circumstances to persuade the jury to sentence Smith to death, while the defense will note the major depression and other trauma in her life as mitigating factors for the killings.
A life sentence would make Smith ineligible for parole until 2024. A death sentence would make her the only woman ever to be executed in South Carolina, and only the state's fifth execution since 1976 when the U.S. Supreme Court upheld the constitutionality of capital punishment.
If the jury hands down a death sentence, an appeal would automatically be entered for Smith in South Carolina's appellate court system -- the first step of a long appeals process that often ends at the Supreme Court.
Defense lawyer David Bruck said the defense would attempt to advance the jury's understanding of Smith's hardships. "There's more to tell about this story," he said.
So far, the jury has heard of her bouts with mental illness, major depression and suicidal tendencies since age 13, and allegations of sexual abuse.
Throughout the trial, Bruck's defense team has portrayed the former secretary as extremely remorseful for killing Michael, 3, and Alex, 14 months, telling jurors her motive was suicide the night she went to the lake.
But prosecutor Tommy Pope said he would continue to emphasize the two toddlers were killed by one person: their mother.
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