(CNN) – Rep. Dennis Kucinich said he supports same-sex marriages, but two other Democrats in Monday night's CNN/YouTube debate said they would only go as far as backing civil unions for gay and lesbian couples.

In response to a lesbian couple from New York, Kucinich, of Ohio, said he would allow gay couples to be married because "if our Constitution really means what it says, that all are created equal."

"Our brothers and sisters who happen to be gay, lesbian or bisexual or transgendered should have the same rights accorded to them and that includes the ability to have a civil marriage ceremony," he said.

Meanwhile, Sen. Chris Dodd of Connecticut and New Mexico Gov. Bill Richardson they would support civil unions — but not marriage.

Dodd supported the Defense of Marriage Act, the 1996 law that denied federal recognition to same-sex marriages and allows states to disregard same-sex marriages licensed in other states. But he said he takes the issue "very seriously."

"I would ask, how would I want my two daughters treated if they had a different sexual orientation from their parents? Better jobs, equal opportunities, to retire, to be with each other," said Dodd, whose daughters are 5 and 2.

Richardson said he supported what is "achievable," which would be "full civil unions with full marriage rights." He said he would not tolerate any discrimination in his administration and would eliminate the current "Don't Ask, Don't Tell" policy that bars gays and lesbians from serving openly in the U.S. military.

– CNN Associate Producer Natalie Apsell