House Republicans this weekend are keeping their focus on efforts to do away with President Obama's signature healthcare reform law.

In their weekly radio address, the GOP trumpeted legislation, passed Thursday, that would eliminate the federal subsidies for low and middle-income Americans when they buy insurance plans – a central pillar of the Democrats' 2010 law.

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Rep.(R-Tenn.), the sponsor of the bill who delivered Saturday’s address, said her proposal is a common-sense solution to fighting fraud.

"Protecting taxpayer dollars is one of Washington’s most important responsibilities. Your money should be spent wisely or not at all," Black said. "And everything we do to stop waste and fix broken government removes obstacles to creating jobs and building a stronger economy."

Black's bill is a response to a rule, issued in July by the Department of Health and Human Services (HHS), that gives state-run health insurance exchanges some flexibility when considering who qualifies for the federal help.

Republicans charge that the rule would hike taxpayer costs by allowing ineligible people to get subsidies. Instead, they want to eliminate all the subsidies until a better verification system is in place.

"They just want to rely on the honor system," Black said. "You heard that right: instead of exercising common sense and accountability, the administration is willing to just give away your tax dollars – no questions asked."

Black characterized the rule as a desperate attempt by the administration "to prop up its struggling health care law."

"Not only is that unfair to hardworking taxpayers like you, it opens the door a mile wide to fraud and abuse," she said.

The Obama administration argues that a robust system is in place to verify eligibility for the subsidies, and the state flexibility will apply only to a small percentage of applicants.

Democrats have pounced on the Republicans' efforts to repeal ObamaCare, noting that the law was passed by Congress, signed by the president and upheld by the Supreme Court. They contend Republicans are frittering precious time that would be better spent on legislation to create jobs, reform the nation's immigration system and ensure the government doesn't shutdown on Oct. 1.

House Minority Leader Nancy Pelosi (D-Calif.) called Black's bill "a desperate attempt to throw a monkey wrench into implementation of the health care law just 19 days before enrollment begins." And Senate Majority Leader Harry Reid Harry Mason ReidSenate Republicans signal openness to working with Biden Mellman: The likely voter sham Bottom line MORE (D-Nev.) said Thursday that he told House Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio) that "all these things they're trying to do on the 'ObamaCare' is just a waste of their time."

"If they want to work with us to improve 'ObamaCare,' let's do it, but not in these guerrilla attacks," Reid said.

Black's bill passed the House by a vote of 235-191, with five Democrats supporting it. The proposal will almost certainly be ignored by the Democratically-controlled Senate.