Canyon County Third District Judge Molly Huskey asked jurors to determine first whether Higgins is guilty of first-degree murder.
If they cant convict him of that charge, Huskey told them to consider second-degree murder.
Prosecutors have argued that Higgins deliberately killed Groat, 27, and that the murder was premeditated. Those are both elements of first-degree murder, but not second-degree murder.
In order to convict, the 12 jurors who began deliberating shortly after 1 p.m. Wednesday must unanimously find Higgins guilty.
Deputy Canyon County Prosecutor Monica Morrison told jurors during closing arguments earlier Wednesday they would have to "discount every piece of evidence in this case" to find Higgins not guilty of first-degree murder.
The two co-defendants who testified that they watched as Higgins shot Groat once in the head and four times in his torso in the early hours of Aug. 27, 2012, were compelling witnesses, Morrison said.
Although the defense blamed Christopher "Mikey" Duran and Cruz Flores for Groat's death, Morrison said the two men face serious punishment anyway for admitting they accompanied Higgins to a remote spot near Lake Lowell and did nothing to prevent the murder.
"If Cruz and Mike were out to frame the defendant, don't you think they would have come up with a better story that wouldn't implicate themselves?" Morrison asked.
She said Higgins sent an incriminating text message after the murder. It ordered Duran, she said, to delete all messages on his phone, Morrison said.
Morrison played a short video segment from a police interview with Higgins four days after the murder. In it, Higgins told a detective he didn't know how his shovel ended up at the murder scene in an isolated area near Lake Lowell in Nampa.
A few months later, Higgins said the shovel had been outside his house and that someone might have taken it.
Duran testified last week that Higgins told him to grab the shovel and place it in the trunk of Groat's car.
He said Higgins suspected Groat had snitched to police about a marijuana deal that Higgins was later arrested for.
Defense attorney Chuck Peterson said that during police questioning about the murder, Higgins told a detective he knew who had turned him in for the drug deal and that it wasnt Groat.
Duran said Groat was lured to Lake Lowell on the guise of serving as a backup for a drug deal that Higgins was carrying out.
Duran, who was charged originally with first-degree murder in the case but had his charge reduced to second-degree murder in exchange for his testimony, said he understood before they left for the lake in Groat's car that Groat would be killed.
The defense claimed Higgins was not present when Groat was killed and that Duran and Flores framed him to save themselves.
Peterson claimed Duran was having illegal sex with an underage girl and that he learned Groat was going to report him to police.
Peterson spent his closing argument trying to cast doubt on the prosecution's claims.
He questioned why no blood was found between the two holes where Groat was reportedly told to dig his own grave, then shot, and the spot 20 feet away where his body was found.