WASHINGTON -- The House of Representatives has signed a contract to pay a law firm up to $500,000 (and possibly more) to defend the Defense of Marriage Act (DOMA) in federal court. But there's a problem with this arrangement: No one seems to know where that money is going to come from, and at least one lawmaker believes House Republicans may be violating federal law.

In March, the House Bipartisan Legal Advisory Group (BLAG) voted along party lines to defend DOMA, the federal law that defines marriage as between one man and one woman. Its decision came after Attorney General Eric Holder announced the administration would no longer argue in support of the law after it concluded that the law is unconstitutional.

At the behest of Speaker John Boehner (R-Ohio), the House General Counsel has signed a contract with former solicitor general Paul Clement to pay his firm, Bancroft PLLC, at a rate of $520 per hour for the case. If expenses go above the cap of $500,000, there is the opportunity to raise it.

But where is this money coming from?

BLAG has no budget, since it's not an actual committee. Congress has not specifically appropriated $500,000 for this case. Boehner first asked the Justice Department to hand over "the funds it would have otherwise expended defending the constitutionality of DOMA" in April, but the agency has so far given no indication it will agree to his repeated requests. (Attorney General Eric Holder has also said the Justice Department wouldn't have spent much on it anyway, since it would have been done by career employees of the government.)

The mystery deepened during a House Legislative Branch Appropriations Subcommittee hearing on Thursday.

Rep. Michael Honda (D-Calif.) pressed House General Counsel Kerry Kircher on the matter. Although the contract states that "the General Counsel agrees to pay the Contractor for all contractual services," Kircher said he was told by the House Republican leadership that no funds would come out of the Office of General Counsel's budget for this purpose.

Dan Strodel, the House's chief administrative officer, is the man who, according to Honda's office, would ultimately write the checks to Brancroft PLLC. But at the hearing, he also said he had no knowledge of where the money would come from.

"Given Rep. Honda's concern, I hope he will join us in efforts to recoup any costs from the Department of Justice -- which is supposed to be defending the law in the first place," said Boehner spokesman Michael Steel.

Honda believes that Boehner's agreement could be violating the Antideficiency Act, which prohibits "involving the government in any obligation to pay money before funds have been appropriated for that purpose." Knowingly violating the law could lead to being fined or imprisoned.

A source familiar with House finances told The Huffington Post that Honda may have a case. The House General Counsel signed the contract and agreed to pay the funds. But since he has admitted that his office doesn't have the money for this case, House leadership would have to have the funds reprogrammed or transferred from other House accounts. The source said that transfer should have been executed before Kircher signed the contract with Clement and Bancroft.

"The budget is tight for the House," said a Democratic Appropriations Committee aide. "All funds are pretty well accounted for. Trying to find $500,000 is not easy with the House budget as tightly wound as it is."

On April 26, the three Democratic members of the Committee on House Administration wrote to Boehner, concerned about the source of the funding.

"How much of the cost will be borne by the budget of the House General Counsel?" wrote Reps. Robert Brady (D-Pa.), Zoe Lofgren (D-Calif.) and Charles Gonzalez (D-Texas). "This Committee is aware that the office of the General Counsel does not have $500,000, let alone the millions of taxpayer dollars which may be required to defend at least 12 DOMA-related lawsuits. If funding for the contract is reprogrammed or transferred from another source, what is that source and what is the approval authority?"

Clement originally took up the case while a partner at the law firm King & Spalding. But after receiving significant public criticism from LGBT rights organizations, the firm filed a motion to withdraw its representation, arguing "the process used for vetting this engagement was inadequate." Attorneys at King & Spalding have since said Clement never submitted the contract to the business review committee for approval. Clement quickly left the firm and joined Bancroft, where he continues to represent the House in the DOMA case.

Bancroft founder Viet Dinh isn't sweating it, though.

"We have no doubt that the House of Representative is good for its word, and no problems representing the American people under the contract," he said in a statement to The Huffington Post.