Both the House and Senate are considering legislation to repeal the Defense of Marriage Act, a federal law that recognizes marriage as a legal union between one man and one woman.
Wednesday, the Senate Judiciary Committee held a hearing to discuss the pros and cons of the Respect for Marriage Act. The bill was introduced by Sen. Dianne Feinstein, D-Calif., to overturn DOMA.
Supporters of DOMA argued that traditional marriage needs legal protection.
"DOMA was passed in '96 because Congress and President Clinton understood that civil society has an interest in maintaining and protecting the institution of heterosexual marriage," Rep. Steve King, R-Iowa, said. "Because it has a deep and abiding interest in encouraging responsible procreation and child rearing."
But opponents say the law unfairly discriminates against same-sex couples.
"Nothing in this bill would obligate any person, religious organization, state, or locality to perform a marriage between two persons of the same sex," Sen. Patrick Leahy, D-Vt., said at the opening of Wednesday's hearing.
"What would change, and what must change, is the federal government's treatment of state-sanctioned marriage," he added. "The time has come for the federal government to recognize that these married couples deserve the same legal protections afforded to opposite-sex married couples."
Wednesday's hearing comes one day after the White House endorsed Feinstein's measure.
President Obama has previously said DOMA is unconstitutional and ordered the Justice Department to stop defending the legislation in court.
Still, before Tuesday he'd never outright endorsed a bill to end DOMA.
"The president has long called for a legislative repeal of the so-called Defense of Marriage Act, which continues to have a real impact on the lives of real people -- our families, friends and neighbors," White House spokesman Shin Inouye said.
Press Secretary Jay Carney added that Obama is "proud to support" the legislation.
Gay rights groups praised the president for his support of the new bill.
"He joins the large and growing chorus urging for an end to DOMA, a discriminatory, unjust and far-reaching law," one group said.
Congress passed DOMA in 1996. Former President Bill Clinton signed the bill into law.