The House on Wednesday advanced two pieces of legislation that are meant to put more pressure on the Obama administration to enforce laws passed by Congress, and not waiver portions it wants to waive for political or other reasons.

In a 229-192 vote, members approved a rule that will govern debate and votes on these two bills Wednesday and Thursday.

One bill is the ENFORCE Act, H.R. 4138, which would allow the House or Senate to file a lawsuit against the administration for failing to enforce laws. Republicans said during the rule debate that this check against the Obama administration is needed because of the various enforcement waivers under ObamaCare, and the immigration flexibility Obama granted some illegal residents in 2011.

"Every day, it seems the President is using more and more unilateral actions to achieve his agenda," said Rep. Richard Nugent (R-Fla.).

"What we're concerned with is… the blanket policy of non-enforcement," he added. "And in some instances, the President isn't just ignoring enforcement of the laws, he is effectively re-writing them."

Rep. Jeff Duncan (R-S.C.) said Obama has an "appalling lack of concern" for laws passed by Congress.

"He expects Vladimir Putin to respect international law with respect to the Ukraine, while the President himself, at the same time, continues to disregard the laws passed by the United States Congress," Duncan said.

Another bill covered by the rule is the Faithful Execution of the Law Act, H.R. 3973. This bill would require federal agencies to report to Congress when they are not following the law.

During the rule debate, Rep. Jim McGovern (D-Mass.) argued that the bills are another example of GOP partisanship, and that the House should be focusing on bills to create jobs. He also accused the GOP of essentially using the bills to stage a press event on the House floor.

"This is a press conference that my friend should have outside of this great building, quite frankly," he said.

Earlier in the day, the White House said President Obama would veto both bills if they were presented for his signature. The White House said the bill authorizing lawsuits would violate the Constitution, and said requiring reporting on legal enforcement would unnecessarily burden federal agencies.