The case marks the first time the justices will consider the First Amendment implications of the program, similar to other programs across the county, and whether the speech depicted on the plates is government speech or the speech of the driver.

In Texas, individuals can choose to have standard issue plates, or pay a fee and design a plate that is subject to the approval of the state. It can be rejected if state officials find it offensive.

READ: Supreme Court takes on specialty license plates

In court, Texas Solicitor General Scott A. Keller stressed the messages on the licenses plates constitute government speech. He said the state "etches its name onto each license plate" and that the law gives Texas the "sole control and final approval authority over everything that appears on a license plate."

Mary-Rose Papandrea, a constitutional law professor at Boston College Law School, said that "in general the free speech clause of the First Amendment does not apply when the government is speaking."

"The only check on what the government can say is the political process, " she said.

But Keller ran into skeptical questions.

Chief Justice John Roberts, for example, expressed doubt that the license plate program constitutes government speech. He said there is no coherent government message but instead it seems like they are "only doing this to get the money."

Justice Ruth Bader Ginsburg pointed to one plate that says "Mighty fine Burgers".

"Is it government speech to say 'Mighty fine Burgers' to advertise a product?" she asked.

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Supreme Court skeptical of specialty license plate case