House Republicans haven’t yet coalesced around a strategy to counter the Supreme Court’s decision to strike down the Defense of Marriage Act, with one member of the party’s conservative wing talking up a doomed effort to amend the Constitution while leadership seems resigned to leave the issue to the states.

In a news conference early Wednesday afternoon, more than a dozen socially conservative GOP rank-and-file members gathered to vent at the court.

But only Rep. Tim Huelskamp, R-Kan., articulated possible next steps, which he says he is already putting into action: introducing a constitutional amendment to limit marriage in the United States to between one man and one woman.

“I’m beginning discussions with my colleagues, but clearly the federal marriage amendment is where we need to be heading,” Huelskamp told reporters following the lawmakers’ formal presentation, during which he alluded to possible legislative remedies.

The last time the House considered a federal marriage amendment on the floor of the chamber was in 2006; it failed then, despite the support of President George W. Bush, and it’s certain to lose again this time around.

But there’s not much else for opponents to do now that the court has ruled.

Members did not take questions after their remarks, but Huelskamp stayed back to elaborate on his amendment strategy. He said he had already requested that aides begin drawing up language for a possible bill and said “hopefully this week” he will begin to gather some co-sponsors.

“The court would like to think this goes away,” he said. “They set the stage for more.”

With a busy legislative agenda, the sense of finality about a Supreme Court decision and how difficult it is to pass a constitutional amendment — let alone have it ratified by the states — it’s unclear when, or even if, House GOP leadership would agree to bring such a measure to the House floor.

Plus, Huelskamp has little pull with leaders, given he was booted off committees last year after they determined he was not a team player. Additionally, Huelskamp was one of a small group of GOP lawmakers to vote against John A. Boehner of Ohio becoming speaker in January.

“We’ll review the proposal at the appropriate time,” a leadership aide said.

Still, the statements issued by Republican leaders themselves were subdued and pointed to the states as the place for the debate.

“A robust national debate over marriage will continue in the public square, and it is my hope that states will define marriage as the union between one man and one woman,” Boehner said.

“I’m disappointed in this decision, and the marriage debate will continue in the states,” said Majority Leader Eric Cantor, R-Va.

Rep. Justin Amash, R-Mich., also privately warned Republicans not to say anything stupid after the ruling, noting that many young conservatives support gay marriage.

Even Rep. Steve Scalise, R-La., the chairman of the Republican Study Committee, didn’t indicate an immediate appetite for pursuing a legislative remedy.

“The Supreme Court has commandeered the role of voters and their elected representatives, and turned the definition of marriage over to unelected judges where this will now be litigated in the courts for years to come,” he said.

Conservative members at the briefing, among them Reps. Michele Bachmann of Minnesota and Tim Walberg of Michigan, called the ruling harmful for children who deserve a mother and a father and devastating for the history of “traditional” marriage. Bachmann added that America today would be rendered unrecognizable to the Founding Fathers.

Rep. Doug LaMalfa, R-Calif., said it would put an onus on churches to perform same-sex marriage ceremonies even if it went against their spiritual inclinations.

All members decried the decision as an overreach by “activist” members of the Supreme Court, whom Rep. Louie Gohmert, R-Texas, called an “unholy quintet.”

And while Rep. Joe Pitts, R-Pa., did stand up to “personally thank Speaker Boehner for defending the House of Representatives and the democratically passed law,” Democrats slammed Republicans for wasting millions of dollars on defense of the law.

“Today … puts to an end House Republicans’ continued waste of millions of taxpayer dollars in their effort to defend their unconstitutional Defense of Marriage Act,” said Rep. Debbie Wasserman Schultz, D-Fla., chairwoman of the Democratic National Committee and ranking member on the Legislative Branch Appropriations Subcommittee, from which account the money has been expended. “Today’s ruling marked the seventh time that House Republicans were defeated in court, wasting $2.3 million of Americans’ hard-earned tax dollars in their quest to defend inequality.”

“It’s really clear now that Republicans wasted that money … instead of focusing on jobs and the economy,” said Rep. Mark Takano, an openly gay freshman Democrat from California who stood outside the Supreme Court with the throngs of activists to receive word of the decision.

Though the money came out of the House’s budget, Boehner and other Republicans have suggested that one day the Justice Department would be compelled to pick up the tab — after all, they have argued, that agency should have been defending the law of the land all along.

So far there have not been efforts to take the money out of the legislative branch appropriation bill’s budget and into that of the spending measure for Commerce, Justice and Science. With the Supreme Court’s ruling, the fiscal 2014 appropriations cycle could be tempered by a fight over whether now is the time for the Justice Department to shoulder that financial burden.

Though it’s unclear now whether anyone has any plans to pursue such a plan, Rep. Jared Polis, D-Colo., said it was somewhat irrelevant.

“Republicans are still trying to foot taxpayers with the bill,” said Polis, another openly gay lawmaker. “I don’t think most Americans are really concerned whether this comes out of the legislative budget or the executive budget.”

Matt Fuller contributed to this report.