Yet foes promptly dismissed the changes as inadequate, and predicted that the measure would fall far short of a needed two-thirds vote in the Senate and the House of Representatives.
The revised proposal, like the original, would define marriage as between a man and a woman. But new language, backers said, would specifically allow state legislatures to continue to determine what benefits same-sex couples could get.
On the eve of a Senate Judiciary Committee (news - web sites) hearing on the proposed amendment, Republican Sen. Wayne Allard (news, bio, voting record) of Colorado, the measure's chief sponsor, unveiled the revisions at a Capitol Hill news conference.
"The new language makes the intent of the legislation even clearer -- to protect marriage in this country as the union between a man and a woman, and to reinforce the authority of state legislatures to determine benefits issues related to civil unions or domestic partnerships," Allard said.
Christopher Anders, legislative counsel for the American Civil Liberties Union (news - web sites), fired back, "This is an act of political desperation."
"The backers of this amendment realize that they don't even have a simple majority of either chamber," Anders said in a telephone interview, adding that the revised language could still jeopardize some rights of gay couples.
Republican President Bush (news - web sites) called on Congress to approve a constitutional amendment to ban gay marriage last month after Massachusetts' highest court ruled gay couples had a right to wed and after marriages licenses were issued to same-sex couples in San Francisco.
While Bush's conservative base applauded his action, many members of Congress have voiced concern about tinkering with the Constitution.
U.S. Sen. John Kerry (news - web sites) of Massachusetts, the presumptive 2004 Democratic presidential nominee, opposes a constitutional amendment. He supports civil unions that can provide couples some of the same legal protections that married spouses enjoy.
Polls show most Americans oppose same-sex marriage, but rather split on civil unions, and many believe the states should handle the matter.
While Allard has the only proposed amendment before the Judiciary Committee, others are expected to prevent "activist" judges and local officials from permitting same-sex marriage.
"Renegade judges and some local officials are attempting to radically redefine marriage," Republican Sen. John Cornyn of Texas, chairman of the Judiciary subcommittee on the Constitution, warned on Monday.
Speaking on the Senate floor, Cornyn, who will chair Tuesday's hearing, said, "We have a duty ... not (to) let extremists in the courts or outside of them reshape society."