Supporters of Melissa Lucio launched a new approach outside the federal courthouse in Brownsville on Saturday. 

Supporters are calling on taxpayers to oppose spending county resources on a new trial for Lucio, saying the county can't win it. 

"We're asking Cameron County to stop wasting our tax dollars and free Melissa Lucio now," one supporter said. 

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Lucio's execution was delayed by a state appeals court late last month.

Lucio remains on death row following the murder conviction for the death of her 2-year-old daughter.

RELATED: Experts: Melissa Lucio faces tough fight to get new trial  

Prosecutors say she beat the girl to death.

Lucio, her legal team and supporters say the child died after a fall down a flight of stairs.