House Speaker John Boehner (R-Ohio) said at a press conference Thursday that he has "no plans at this point" to press forward with a bill that would replace the federal Defense of Marriage Act.

Boehner said there are “no plans at this point in terms of how the House will move ahead on this.”

House conservatives signaled after Wednesday's Supreme Court decision striking down a key portion of the law that they would move forward with a constitutional amendment to reinstate it. But the party as a whole hasn't yet indicated a strong willingness to rehash the gay marriage issue, as a growing majority of Americans now support it.

The portion of the law that was struck down defined marriage, for the purposes of the federal government, as being between one man and one woman. The House GOP leadership sued to force the Obama Administration to defend the law after the Justice Department opted not to.

Boehner defended that decision and the use of taxpayer funds to do so.

"The president or the attorney general doesn't have the right to declare a law unconstitutional; only the Supreme Court does," Boehner said. "And so I believe that the House's actions were appropriate. The court's made its decision."

Boehner issued a statement after Wednesday's ruling that said he was "disappointed" with the court's decision but also that it was the result of the checks and balances of American government.