"We want to preserve people's voting rights, but county clerks of New Mexico, the local voting authorities, want to preserve safety with the public," Ivey-Soto said.

The Republican Party of New Mexico, represented by Carter Harrison, believes a complete mail-in election is illegal in the state.

"What the petitioner is asking you to do is not interpret the law, but go and make something legal," he said.

The justices had questions for both sides.

They wanted to know why people couldn't just ask for an absentee ballot. The court also questioned whether it even has the power to re-write election laws since neither the state's constitution, nor the legislature, have ever addressed the issue before.

"I think we are trying to usurp the legislature and give the secretary of state powers she doesn't have," said Chief Justice Judith Nakumira.

The state Supreme Court ordered the secretary of state and county clerks to send absentee ballot applications to all voters, so more people can vote with an absentee ballot-- rather than in-person.