"The question before this court is whether the Constitution puts a stop to that ongoing democratic debate and answers this question for all 50 states," Cooper argued.
Olson argued that Proposition 8 "was stigmatizing a class of Californians based upon their status and labeling their most cherished relationships as second-rate, different, unequal and not OK."
He sparred with Justice Antonin Scalia, who made little secret of his disagreement with Olson's contentions.
"When did it become unconstitutional to exclude homosexual couples from marriage?" Scalia asked. "1791? 1868, when the 14th Amendment was adopted?"
Olson responded with his own rhetorical questions, alluding to landmark Supreme Court decisions on race discrimination.
"When did it become unconstitutional to prohibit interracial marriage?" Olson asked. "When did it become unconstitutional to assign children to separate schools?"
Scalia said the answers to those questions were easy ones. "At the time that the equal protection clause was adopted," he said, before adding, "but don't give me a question to my question."
When Scalia repeated his question later, Olson responded, "You've never required that before."
Support for gay marriage has soared in recent years. A Pew Research Center poll released last week found that 49 percent of adults supported legalization, with 44 percent opposed. Ten years earlier a Pew poll found 33 percent in support, with 58 percent opposed. The latest poll had a margin of error of plus or minus 3 percentage points.
Californians back gay marriage by almost 2-1, with 61 percent supporting it and 32 percent opposed, according to a Field Poll released last month. That survey had a margin of error of plus or minus 3.5 percentage points.
Tuesday's session was exactly a year after the justices heard the first day of arguments on Obama's health-care law.
— With assistance from Nick Taborek in Washington.