The lawsuit claims the Obama administration set up a "giveaway" of billions of dollars to the insurance industry under the landmark law. Chip Somodevilla/Getty Images

Republican members of the U.S. House of Representatives on Friday finally made good on their promise to sue the Obama administration over what they see as executive overreach during the implementation of the Affordable Care Act. The move comes at a highly sensitive time for the relationship between the executive and legislative branches, as Obama weathers intense GOP scrutiny for the immigration policy overhaul he announced Thursday night.

“Time after time, the president has chosen to ignore the will of the American people and rewrite federal law on his own without a vote of Congress," House Speaker John Boehner said in a statement. "That’s not the way our system of government was designed to work. If this president can get away with making his own laws, future presidents will have the ability to as well. The House has an obligation to stand up for the Constitution, and that is exactly why we are pursuing this course of action.”

The lawsuit asserts that the Obama administration set up a "giveaway" of billions of dollars to the insurance industry under the landmark law, also known as Obamacare, according to Boehner's statement. That accusation reflects a Congressional Budget Office estimate that, under Obamacare, the administration will pay approximately $175 billion over 10 years to health care insurance companies -- money that Congress has not appropriated.

"The administration is instead unlawfully and unconstitutionally using funds from a separate Treasury Department account – authorized for other purposes – to pay insurance companies and thereby unilaterally altering the structure of the health care law," according to Boehner.

The lawsuit also claims the administration made the "unilateral decision to twice waive the health care law’s employer mandate," which was supposed to begin in January. The GOP suit claims Obama illegally delayed the implementation of that mandate, which requires companies employing 50 or more full-time workers to offer those full-time employees health insurance options or be penalized.

The lawsuit was filed against the secretaries of the departments of Health and Human Services and Treasury, and was the culmination of months of threats.

House Minority Leader Nancy Pelosi was quick to respond Friday with a statement of her own, decrying the lawsuit.

“The fact is, this lawsuit is a bald-faced attempt to achieve what Republicans have been unable to achieve through the political process," she said. "The legislative branch cannot sue simply because they disagree with the way a law passed by a different Congress has been implemented. It is clear, as one leading legal scholar put it, that this lawsuit is ‘an embarrassing loser.’"

The House voted 225-201 along party lines to authorize the lawsuit on July 30, according to Reuters. A number of delays led to its filing being pushed back past the November election. One reason for the delay was the resignation of two lawyers hired by Boehner to take on the case against the president.

The filing of the lawsuit did not come as a major surprise given the months of threats. Boehner said Tuesday that he hired Jonathan Turley, a prominent constitutional law professor at George Washington University, to advance the lawsuit, the Atlantic reported.

The lawsuit was filed just a day after Obama circumvented Congress on another hot-button issue, immigration, by exercising the powers of his office to take executive action to help fix the long-festering problem. The move was seen by many as a direct provocation of Republicans in Congress, and the Obamacare lawsuit just adds tension to an already fraught relationship. The Affordable Care Act suit differs from any move over immigration in that Congress actually passed the health care law, while the immigration move was a unilateral step by the Obama administration.

“Instead of working together to fix our broken immigration system, the president says he’s acting on his own," Boehner said Thursday. "The president has said before that ‘he’s not king’ and he’s ‘not an emperor,’ but he’s sure acting like one. And he’s doing it at a time when the American people want nothing more than for us to work together.”

Republicans said that the lawsuit may be amended to include a portion regarding Obama's immigration policies, or they could file a separate lawsuit focused on Obama allegedly abusing his power to force changes in immigration policy.