The House this week will easily pass a proposal to change to Obamacare that has sound bipartisan support, a trait that gives it a real chance of becoming law even in the face of Democratic demands that debate over the law should be “over.”

The Obama administration and its Democratic allies in Congress will of course continue to resist all efforts to repeal the law entirely. But in the midst of that simplistic debate over “repeal,” House Republicans continue to call up smaller tweaks to the health care law, and a few handfuls of those bills have actually been signed by the president over the past few years.

House Will Vote to Change Obamacare With Democratic Support | Obamacare Vote

House Speaker John Boehner of Ohio walks to a GOP caucus on Capitol Hill in Washington, Wednesday, April 2, 2014. GOP leaders are on pace to pass an Obamacare tweak that has support from Democrats. (AP Photo/J. Scott Applewhite)

This week, the House GOP leaders will call up a bill that could make it into that exclusive club. On Tuesday, members are expected to pass the Expatriate Health Coverage Clarification Act, H.R. 4414. The bill would exempt companies and expatriate workers from Obamacare’s rules, and the lead sponsor is a Democrat.

The idea behind the bill is that people working outside their home country often receive high-end health coverage through plans specifically designed for expatriates.

“Expatriate health insurance plans offer high-end, robust coverage to executives and others working outside their home country, giving them access to a global network of health care providers,” said Rep. John Carney (D-Del.) when he introduced his bill.

But if Obamacare’s rules were to apply to U.S. insurance companies offering these plans, those rules would likely raise costs and put non-U.S. insurance companies at a competitive advantage. Members of both parties agree that these plans should therefore be exempt from Obamacare, and the bill is likely to pass easily by Tuesday evening.

Earlier this month, the House voted 257-159 in favor of the bill, but it failed because Republicans used a faster process that required a two-thirds majority vote. But that vote saw 52 Democrats support the bill, which means it will easily pass Tuesday when just a simple majority is needed.

Despite the constant bipartisan fighting over Obamacare, the law has changed frequently it was passed in 2010. Many of the big changes have come from the Obama administration itself – for example, the White House has delayed both the requirement for companies to provide health insurance a few times, as well as the individual mandate to buy insurance.

But several other changes have been led by the GOP-controlled House, and most of these were clearly bipartisan and signed quickly by President Obama. A famous early example was the repeal of the so-called “1099″ requirement, which would have had all companies file tax forms whenever they pay out $600 or more to a contractor or service provider.

That was seen as a monster paperwork requirement that was meant to help fund the law, but both parties agreed it was excessive and quickly ended it.

Republicans also passed a bill to repeal a withholding tax that would have hurt small companies, legislation to end a failed attempt to create nonprofit health “co-ops,” and a few bills to cut into the Prevention and Public Health fund, which the GOP called a “slush fund” that was being used for things not directly related to healthcare, like building bike paths.

Earlier this year, the House quietly agreed to language that gave companies more flexibility to offer insurance plans with high deductibles. ObamaCare had put caps on these deductibles, and most agreed the caps should go – the Obama administration had even waived enforcement of the caps in the meantime.

This week’s expatriate bill seems to have a good shot at passing the Senate once it clears the House this week. If so, it will give Republicans another success story to justify continued scrutiny of Obamacare, the law that – four years later, and despite White House protest – still invites debate.