WASHINGTON — A skeptical federal judge grilled Obama administration lawyers Thursday over House Republicans’ health care lawsuit, sounding unlikely to side with the president and dismiss the case.

“You don’t really think that, do you?” U.S. District Judge Rosemary Collyer asked Justice Department attorney Joel McElvain in the opening moments of his argument, as he tried to assert that the House hadn’t suffered a particular injury from Obama’s health care law and therefore lacks a basis for suing.

“I have a very hard time taking that statement seriously,” Collyer said. At other points she chided McElvain for his responses, saying “You are dodging my question” and “You may disagree with me but I happen to be the judge.”

At issue in the case is about $175 billion that the administration is paying health insurance companies over a decade to reimburse them for offering lowered rates for poor people. The House argues that Congress never specifically appropriated that money, and indeed denied an administration request for it, but that the administration is paying it anyway.

The House says this amounts to unconstitutionally co-opting Congress’ power of the purse. The administration insists it is relying on an existing pot of money that it is allowed to use.

Thursday’s hearing focused on whether the House has legal standing to bring the suit at all. The administration says it doesn’t, arguing the House has not been injured and is just advancing abstract complaints about implementation of the law. The administration argues the House has many other remedies available, such as passing a new law.

“The House cannot sue the executive branch over the implementation of existing federal law,” McElvain insisted, adding later, “Nothing limits the right to come back and enact new legislation.”

George Washington University law professor Jonathan Turley, arguing for the House, vehemently disagreed.

“We believe we have established what can only be viewed as a concrete injury,” Turley said, at one point brandishing a pocket-sized copy of the Constitution. “I find it astonishing that this can be viewed as an abstraction.”

Frustrated House Republicans authorized the lawsuit over Democratic objections last summer, in the run-up to the congressional midterm elections. They had already voted dozens of times to repeal all or parts of the law known as Obamacare, but as long as President Obama is in the White House they have no legislative solution.

It’s not clear whether the House suit will make it that far. Previous attempts by members of Congress to sue past administrations have been tossed out, although the House health lawsuit is the first by the full House against a sitting president.