Democrats and Republicans in the Senate are haggling over how to offset the cost of an extension of long-term unemployment benefits—and have settled upon one method that advocates are calling needlessly cruel to some disabled Americans.

Republicans have proposed, and Democrats appear to have accepted, a measure that prohibits people from collecting Social Security’s disability insurance at the same time they collect unemployment benefits. This aims to save $100 million per year.

This idea has long been promoted by conservatives, but was also included in President Obama’s most recent budget. It seems to be based, however, on a misunderstanding (willful or otherwise) of how the two programs work. Here’s the conservative Heritage Foundation with a good distillation of the basic premise:

The conditions for eligibility of the two programs are mutually exclusive: The DI program serves individuals who are deemed physically or mentally unable to work; the UI program replaces some of the lost earnings of those who become unemployed but are otherwise able to work. Thus, people should not be allowed to draw from both programs simultaneously.

Sounds good at first blush—why should people be allowed to double dip? But that’s not what some people who draw from both programs are doing.

To even qualify for disability benefits—which is more difficult in the United States than any other developed country—one has to have worked for at least one-fourth of their adult lives, and five of the last ten years. Given that one has to have a severe impairment to qualify for disability insurance, only a minority of people receiving benefits ever work again.

But a small percentage do—and Congress has actually encouraged them to work. It passed a “substantial gainful activity” provision that allows people on disability insurance to still earn up to $1,070 per month and keep their benefits. The idea is to encourage people who are disabled but can still work at least part-time to do so. That helps the economy, and may help that person transition back into full-time employment, if their medical condition at some point allows it.

Now imagine a person in that situation loses his or her part-time job. Shouldn’t he or she be able to collect unemployment benefits as well, especially since they’ve paid into both programs over the years? If Congress adopts this new measure, the answer would be no.

There are a vanishingly small number of people even in this situation—about 117,000 of the nearly 9 million Americans on disability also collect unemployment insurance. The concurrent benefits average $3,300 total each quarter, which hardly affords one a luxurious lifestyle.

But members of both parties are apparently ready to tell this small segment of the population—people who are both disabled and lost a part-time job—that they are receiving too much money. It’s all in the name of “paying for” an unemployment insurance extension which historically has never had offsetting spending cuts attached. As noted, this measure saves in total $100 million each year, or three-thousandths of a percent of the annual federal budget.

Moreover, advocates for Social Security see a disturbing precedent in raiding the program as a means to pay for other initiatives, even if they are worthy ones. “What’s on the table here is a permanent cut to Social Security in exchange for a temporary extension to a badly needed but unrelated program,” said Rebecca Vallas of the National Organization of Social Security Claimants’ Representatives.

There hasn’t been much pushback on the Senate floor to this provision, though Senator Tom Harkin gave a reliably smart and passionate speech on Monday decrying the proposal.

As of Tuesday afternoon, it seems as if the entire unemployment extension bill may go off the rails, and so people collecting both disability and unemployment benefits may be spared—for now. But there’s clearly bipartisan interest in this idea.