WASHINGTON – Opponents of gay marriage concede victory will not be swift in their attempt to amend the U.S. Constitution, even after prevailing in all 11 states where the issue was on the ballot last month.

While the November 2 election also increased the ranks of amendment supporters in both houses of Congress, the gains were relatively small.

“We’re going to have to see additional court cases come down” supporting gay marriage before congressional sentiment shifts dramatically, predicted John Cornyn, a Republican senator of Texas. Mr. Cornyn supports the amendment that failed in both houses of Congress this year.

Critics of gay marriage have long warned of such court rulings. Cornyn and others who support changing the Constitution to ban gay marriage say several cases have the potential to produce a sharp shift in congressional sentiment toward their viewpoint. They point to suits in Florida, California, Nebraska, and elsewhere.

But Matt Coles of the ACLU’s Lesbian and Gay Rights Project said that’s unlikely – and not entirely by accident.

Many of the cases making their way through the courts were filed by individuals not affiliated with leading gay rights organizations, he said, and were not framed to make a targeted challenge to a 1996 law known as the Defense of Marriage Act.

Frontline groups have held off, he said. “People think that neither the country nor the courts are ready for it and probably we’ll lose. Nobody likes to take cases and lose.”

The 1996 law defines marriage as the union of a man and a woman. It also says no state is required to recognize same-sex marriages sanctioned by any another state.

Purely by the numbers, prospects for passage of an amendment in Congress “have definitely improved” following the election, said Tom Mc-Clusky of the Family Research Council. “But by enough? That’s going to be wait and see.”

Leaders on both sides of the issue say supporters of the amendment gained four votes in the Senate on November 2, and a small, undetermined number in the House. Based on votes in 2004, amendment opponents still have more than enough strength to prevail in a second showdown.

The measure drew 48 Senate votes on a procedural roll call, far below the two-thirds majority needed for passage. The vote in the House was 227-186, 49 less than the required two-thirds.

Passage by Congress would send the issue to state legislatures for ratification. Three-fourths of them also would have to approve it.

It’s not clear how aggressively the White House or Republican leaders in Congress intend to push the issue, with the election over and priorities such as Social Security and tax overhaul competing for attention.

White House political adviser Karl Rove said after the election that President Bush intends to continue seeking a constitutional amendment that says marriage must consist of a man and a woman.

At the same time, GOP congressional aides who attended a series of closed-door meetings recently said Mr. Rove did not mention the amendment when he outlined the administration’s key legislative goals for the year ahead. Nor did the gay marriage issue figure prominently in strategy sessions held by GOP congressional leaders, added these officials, who declined to be identified by name because the proceedings were closed to the press.