The resolution was released Thursday by the House Rules Committee, and if approved by the Republican-controlled chamber, it will be the first time either house of Congress has sued the president for failing to enforce the law.
Speaker John Boehner, R-Ohio, has positioned the move as a defense of institutional roles.
"If this president can get away with making his own laws, future presidents will have the ability to as well," he said in a statement released concurrently with the resolution draft. "The House has an obligation to stand up for the legislative branch, and the Constitution, and that is exactly what we will do."
Despite rumblings from the fringes of his party, and repeated questions from press, Boehner maintains the lawsuit -- and not impeachment proceedings -- is the appropriate course of action.
"This is not about impeachment, this is about faithfully executing the laws of this country," he reiterated earlier this week.
Speaking from an event in Austin, President Obama suggested that he wasn't the one failing to meet the responsibilities of his job description.
"You hear some of them -- 'Sue him,' 'impeach him.' Really? Really? For what? You're going to sue me for doing my job?" he said. "Rather than wage another political stunt that wastes time, wastes taxpayers' money, I've got a better idea: Do something."
Taking a slightly different tack Thursday, Boehner said he wasn't challenging the president's right to take executive action -- admitting Obama's use was actually low for a modern president -- but said some of his executive actions have been tantamount to making his own laws.
"In 2013, the president changed the health care law without a vote of Congress, effectively creating his own law by literally waiving the employer mandate and the penalties for failing to comply with it," Boehner said. "That's not the way our system of government was designed to work. No president should have the power to make laws on his or her own."
The administration has argued its actions have been within its authority to carry out policy in accordance with the laws passed by Congress.