A new Republican majority in the House in 2010 promised to do away with President Barack Obama's signature legislative accomplishment, the Affordable Care Act.

If it couldn't repeal the entire law at once — which it was unlikely to be able to do, with a Democratic Senate and the president still in place — they would repeal it piece by piece, promised a document from House Majority Leader Eric Cantor, "Delivering on Our Commitment.”

"If all of ObamaCare cannot be immediately repealed, then it is my intention to begin repealing it piece by piece, blocking funding for its implementation, and blocking the issuance of the regulations necessary to implement it. In short, it is my intention to use every tool at our disposal to achieve full repeal of ObamaCare.”

House Republicans voted twice to fully repeal the law, and made about 30 other attempts to "defund, change or strike down” parts of it, according to Congressional Quarterly.

Most of those efforts were rebuffed by the Senate.

But the House Speaker's Office pointed us to six bills the president did sign into law, saying each one either peeled back parts of the law or reduced funding.

According to Republicans:

• H.R. 4 reduced health care insurance exchange subsidy payments by $25 billion.

• H.R. 1473 reduced funding for the Consumer Operated and Oriented Plan by $2.2 billion.

• Senate Amendments to H.R. 674 tweaked eligibility rules for certain programs, cutting spending under the health care law by $13 billion.

• H.R. 2055 pulled $400 million from the Consumer Operated and Oriented Plan and $10 million from the Independent Payment Advisory Board, plus reduced funding for the Internal Revenue Service by $305 million. (The IRS will enforce the health care law's individual mandate.)

• H.R. 3630 cut $5 billion from a prevention and public health fund and recouped $2.5 billion in "excess” Medicaid funding for Louisiana.

• H.R. 4348 removed $670 million in Medicaid spending for Louisiana.

Health policy experts say the changes are modest.

"As you can tell from news reports, implementation of health reform is proceeding apace, and lack of funding is not standing in the way,” said Paul Van de Water at the liberal Center on Budget and Policy Priorities.

Michael Tanner, an expert in health care policy at the libertarian Cato Institute, made the same point.

"They did trim some pieces, but pretty minor ones,” Tanner said. "All the key components of Obamacare remain in place: mandates, taxes, subsidies, insurance regulation.”

The changes were consistent with Republicans' promised "piece by piece” strategy. But those pieces weren't big or numerous enough to substantially block "funding for implementation" of the health care law. We rate this Promise Broken.

Republicans vowed during the 2010 campaign to block funding for the health care law, formally known as the Patient Protection and Affordable Care Act. But blocking funding has become complicated as Republicans and Democrats negotiate to finish funding the government for the current fiscal year.

So far, Congress has been passing short-term funding measures, called continuing resolutions or CRs, while negotiations continue over a final budget for fiscal year 2011, which actually started in October 2010.

The short-term measures mean Congress hasn"t addressed many major funding issues, and that"s making some Republicans impatient.

Reps. Steve King, R-Iowa, and Michele Bachmann, R-Minn., recently wrote an open letter to the Republican leadership asking the party leaders to redouble their efforts to block funds for the health care law. King and Bachmann said that the "must pass” legislation for this year should include a repeal of funding that was included in the 2010 law, not just stopping the ongoing funding to implement the law.

Bachmann has repeatedly criticized the health care law for having $105 billion in spending included in it, a claim we"ve previously fact-checked.

The budget negotiations in Congress have served to delay a showdown between Democrats and Republicans over funding for the health care law. But there's been progress on this promise. Because Republicans are actively working to stop funding, we"re rating this promise In the Works.