"The Republicans have taken a bipartisan idea … that would actually put money directly in the pockets of hardworking Americans, and made its passage contingent on a bill that rehashes the healthcare reform debate from the last Congress," Hastings said. "Once again, my colleagues have chosen to play politics with the lives of middle-class and working poor Americans."

Later in the debate, Rep. Bill Keating (D-Mass.) agreed that Republicans are "messing up" a chance to offer bipartisan support for repealing the withholding rule by attaching it to the MAGI bill.

Keating said he would try to offer an amendment that would pay for the repeal of the withholding rule by increasing taxes on oil companies, which he said are receiving billions of dollars in benefits because they are underrated. However, Keating's language is not expected be given any consideration in the House.

Republicans rejected these arguments by pointing out that the healthcare law used a MAGI calculation that would allow middle-class Americans to qualify for Medicaid and other programs meant for those with less income. They also said many Democrats are opposed to this change.

"Changing the income formula could result in individuals whose income is up to 400 percent of the poverty level receiving Medicaid," said Rep. Diane BlackDiane Lynn BlackRyan picks his negotiating team for tax cut bill Overnight Finance: House approves motion to go to tax conference — with drama | GOP leaders to consider Dec. 30 spending bill | Justices skeptical of ban on sports betting | Mulvaney won't fire official who sued him Lawmakers take to Twitter to spread the Thanksgiving cheer MORE (R-Tenn). "This is unacceptable."

While Hastings and Keating tried to argue that the GOP would be taking away healthcare benefits from up to 500,000 Americans, Black also noted that the MAGI change is not scheduled to take effect until 2014, so making the change now does not take any coverage away from anyone.

Other Democrats, such as Reps. Jason Altmire (D-Pa.) and Earl BlumenauerEarl BlumenauerDemocrat: Pelosi ‘ceded the moral high ground’ on sexual harassment Clyburn on disparity in responses to sexual allegations: ‘Who elected them?’ Third House Dem calls for Conyers to resign MORE (D-Ore.), spoke in favor of the change.

The House ended debate on the rule for the two bills shortly after 1 p.m., and was expected to approve the rule later in the day, setting up House passage mostly likely on Thursday.

The withholding rule would require all levels of government to withhold 3 percent of payments made to contracts. The idea was approved as a way to help ensure the collection of tax revenues, but it has never been implemented, and has since been discredited as a burden to federal and state governments that would cost more to implement than the revenue it would generate.