While the tax seems trivial, it has become a major sticking point for Republicans, especially for those whose constituencies include medical device makers like Boston Scientific (BSX) and Medtronic (MDT). To end the standoff, the Obama administration could be persuaded to give up the tax in order to induce enough Republicans to break rank and vote for the “clean” version of the budget bill. That could be a boon for medical device makers, potentially saving them nearly $30 billion over the next 10 years.

The Democrats have waited years for this day. No, not for the start of the government shutdown, which began at midnight, but for the opening of the so-called health care exchanges. As of October 1, it is now possible for Americans to shop a wide variety of health insurance plans armed with a government subsidy. For those (very) few who qualify, the ACA, known pejoratively as Obamacare, will bring health insurance premiums down to earth, allowing more people to afford decent health care coverage.

But there was no cheering in Washington last night, at least not over at the White House. The Republicans had eclipsed President Obama’s big day by shutting the government down. Headlines today are all about the shutdown with the news on the historic health care exchange openings regulated to the proverbial back pages. If the Republicans’ goal throughout the budget battle was simply to rain on the Obama administration’s victory parade, they have succeeded.

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Yet there are members on the far right of the Republican Party who want to push the envelope even further and pressure Democrats to delay implementation of the ACA for a year. The Democrats have said repeatedly that they will not vote for any budget bill that delays implementation of ACA. It would not engage in rounds and rounds of negotiations to “hammer out” a deal, either. Both sides are sticking to their guns here with each side possessing little leverage over the other. This could lead to a prolonged government shutdown, which could end up shaving a few percentage points off of the nation’s economic growth rate for the fourth quarter.

Neither side wants the economy to suffer, at least that is what they both say. Taking that view at face value, is it possible for the two sides to strike out some sort of deal here before the government shutdown gets too bad? Well, it might very well be that the Republicans have been signaling a way out of this mess all along. It turns out that the revised House bill does more than try and “defund” Obamacare; it also calls for the repeal of a proposed tax on medical device makers. The tax is one of many revenue enhancing mechanisms that are supposed to help offset the cost associated with funding the ACA.

Now, the Democrats have said that they will not support lifting the tax under any circumstances, but that seems unlikely now that the Republicans have managed to shut down the federal government. When picking between devils here, lifting the tax seems to be the less painful option and could allow the Republicans to save face.

Therefore it is logical to assume that the medical device maker tax will be either killed or altered in a way to make it acceptable to the industry. The hope here is that this will be just enough “compromise” to recruit Republican lawmakers to break rank and vote alongside Democrats. An estimated 400,000 people work in the industry across a multitude of states and districts so it stands to reason that some Republicans would be inclined to cross the aisle.

MORE: Obama’s safety net didn’t cause the shutdown

“Some of the biggest winners in a repeal would be the orthopedic companies like Stryker (SYK), which is based in Michigan, and Zimmer Holdings (ZMH), based in Indiana,” Tom West, a financial advisor at Signature Estate & Investment Advisors, told Fortune. “These are the largest suppliers of artificial hips, knees, and joints where demand for these products for aging boomers is already sky high.”

It shouldn’t be too hard to get Democrats to sign off on the provision killing the medical device tax, either. Sens. Klobuchar and Franken, both Democrats from Minnesota, along with 17 other Senators have been urging the Democratic leadership to lift the tax. Minnesota is home to Medtronic, 3M (MMM), and St. Jude, as well as a number of other smaller medical device makers. Other big names like Boston Scientific, Baxter International (BAX) and Becton Dickenson (BDX) are located in the Democratic strongholds of Massachusetts, Illinois, and New Jersey, respectively.

The administration is worried that it could be compromising the fiscal soundness of the ACA by giving up the estimated $29 billion in revenue the medical device tax is supposed to raise over the next 10 years. That is a great deal of cash for the medical device community, but it is only a fraction of the estimated $1.7 trillion needed to fund the ACA during the same time. But if you believe the Congressional Budget Office’s projections, subtracting the tax would still leave the program fully funded and in the black by some $80 billion over the next 10 years.

The Republican’s desire to delay implementation of the ACA is truly unreasonable, and they know it. The health care exchanges are up and running today despite the government shutdown. It is simply too late to stop Obamacare. But all is not lost. The Republicans can still walk away winners here if they are able to convince the administration to change their minds on the medical device tax. A repeal would also benefit Democrats and would allow for the system to remain in the black. Given all the devils out there, this seems like the one both sides can live with.