That pledge came in the context of afternoon debate to repeal federal funding for states to set up health insurance exchanges, which prompted repeated complaints from Democrats that Republicans continue to focus on healthcare when they should be focused on job creation.
Democrats also said the exercise is a waste of time because the Senate and White House will not accept it.
"This is another piece of legislation that is going nowhere," House Energy and Commerce Committee ranking member Henry Waxman (D-Calif.) said. "The Senate will never pass it and the president will never sign it."
Rep. Frank Pallone Jr. (D-N.J.) also argued that even if the bill could become law, it would simply strip federal funding for health insurance exchanges and force states to pay for them. Pallone said the exchanges are at the core of last year's healthcare law, and that rescinding federal funds for the exchanges would make it more difficult to deliver benefits to uninsured Americans.
Several Democrats said they were puzzled over why Republicans would be looking to hurt states in this way, since the GOP has traditionally been in favor of states' rights. But Republicans rejected this argument by saying the healthcare law forces states to accept federal mandates to implement the law.
"It's really almost pathetic to think that they're arguing on states' rights because really, the healthcare bill that they're advocating … forces state governments to pay for existing established exchanges," Rep. Cliff Stearns (R-Fla.) said.
Republicans also continued to focus on the federal funding for exchanges, which Health and Human Services Secretary Kathleen Sebelius has said is an unlimited fund she can use. Several Republicans bristled at the idea of giving HHS a blank check to fund state programs.
"The absolute worst thing you can do if you're trying to reduce costs is give the government an unlimited checkbook," Rep. Mike Pompeo (R-Kan.) said. "They will spend it, they will spend it every day, they will spend it all the time."
The Congressional Budget Office has said repealing the federal funding through H.R. 1213 would save more than $14 billion over 10 years, but Republicans argued spending could even exceed those levels, given Sebelius's remarks.
Stearns said allowing this unlimited spending to continue would only increase the risk of a real fiscal crisis.
"Just because we followed Greece into democracy, does not mean that we should follow them into bankruptcy," he said.