Patricia Millett, arguing for a coalition of voters claiming disenfranchisement, told the court the federal law was a "safe harbor" in the face of different, intrusive state laws.
But Kennedy suggested otherwise.
"The state has a very strong and vital interest in the integrity of its elections, even when those -- and perhaps especially when those -- are elections of federal officials," he said. "And it seems to me" the federal appeals court ruling against Arizona last year "did not give sufficient weight to that interest."
Among those bringing suit is Jesus Gonzalez, a public school employee in Yuma who tried to register to vote the day he became a citizen.
His application was twice rejected when his separate naturalization and driver's license numbers were improperly "red-flagged" by state databases that initially indicated he was a non-citizen.
Nina Perales, Gonzales' attorney from the Mexican American Legal Defense and Educational Fund, told CNN that about 31,000 potential voters had their applications rejected in the two years after the Arizona law took effect.
She said 90 percent of those were born in the United States and that only 20 percent were Hispanic.
In her brief with the high court, Perales said voter-registration drives at county fairs, church services and similar venues have fallen off since many potential voters don't bring the necessary citizenship documents -- like a birth certificate -- to these community events.
One estimate found a 45 percent reduction in Maricopa County, the state's largest and seat of the capital, Phoenix.
The Obama administration said if Arizona law was allowed to continue, it would create a mishmash of regulations.
"Each state could impose all manner of its own supplemental requirements beyond the federal form," aid Solicitor General Donald Verrilli Jr. "Those requirements could encompass voluminous documentary or informational demands, and could extend to any eligibility criteria beyond citizenship, such as age, residency, mental competence, or felony history."
But Proposition 200 supporters say the state needs to power to keep illegal immigrants and those ineligible to vote in the United States from getting a ballot.
"I believe we must go out of our way to protect the integrity of America's elections, to avoid the fraud we see regularly in other nations, and which if not checked will rise up here in the United States," said Russell Pearce, a former state senate president, who helped spearhead Prop 200's passage.
The case is Arizona v. Inter Tribal Council of Arizona (12-71). A ruling is expected in three months.