First, meat inspectors got a reprieve from the sequester. Then air-traffic controllers at the Federal Aviation Administration . Now cancer and teachers’ groups are hoping to jump on the slippery slope Congress appears to have created by carving out special status for some programs hurt by automatic spending cuts.

Of course, many groups looking for the same kind of funding flexibility Congress gave to the FAA this week lack the made-for-TV visuals of airplanes stranded on tarmacs.

Still, the American Cancer Society’s affiliated advocacy group is pushing to roll back the sequester’s more than 5 percent cut to the National Institutes of Health. American Cancer Society Cancer Action Network Chris Hansen says research is disproportionately affected by such cuts because the investments in research take place over such a long term.

“They’re actually going to lose a lot of other research that they’ve already funded over the years,” Hansen said in an interview. If investments in existing projects are cut back, the NIH may not be able to track effects on participants in past trials, he explained.

“You’re going to have people that are going to die,” Hansen said of people being tossed from clinical trials.

While White House Press Secretary Jay Carney signaled President Barack Obama would sign the bill the House passed Friday to allow reprogramming of FAA funds to stop air-traffic controller furloughs, Carney cautioned against other “Band-Aid” measures.

“Given how the Congress deliberates and the disagreements that exist on a variety of narrow, specific issues, you can imagine how little would be accomplished if that were the path that were chosen,” Carney said. “The right path is simply to come to the agreement on principle that everybody used to agree on, which is that the sequester should never be implemented.”

Joel Packer, the executive director of the Committee for Education Funding, an organization that counts among its membership major teachers’ unions and public and private university systems, said that eventually the public would see sequester cuts other places, like in classrooms with more students.

“It seems that Congress and the president are hoping that if they fix the FAA problem, sequestration — which will continue to cut funding for critical programs for the next decade under current law — will be out of sight, out of mind, for the American people,” Packer said. “They’re wrong.”

Packer’s group is one of about 3,200 of various sizes that’s been battling against sequestration cuts as part of the NDD United coalition.

While the groups are pushing back against sequester cuts for funding far away from Washington, the NDD acronym stands for non-defense discretionary, a part of the federal budget largely subject to the appropriations process. The NDD sent a letter to members of Congress on Friday opposing the FAA flexibility legislation. The House passed the measure Friday without much opposition after Senate passage by unanimous consent Thursday night.

Of course, discretionary defense spending has been slashed through the sequester cuts as well, a point that Sen. John McCain sought to highlight as the FAA fix passed. The Arizona Republican said that while he supported the narrowly tailored FAA funding flexibility measure, he couldn’t understand the lack of emphasis on the Pentagon budget.

“It is shameful for us to make allowances for the FAA while doing nothing to stop the draconian cuts that are decimating our military today and putting our nation’s security in danger,” he said in a statement. “Dealing with the impacts of sequestration on a case-by-case basis does nothing to fix the underlying issue and prolongs this damaging policy.”

“While Congress gives flexibility to the FAA, our military aircraft don’t fly and our ships don’t sail,” McCain said, echoing comments he made Thursday while speaking off the cuff at a breakfast Thursday.

Hansen, whose résumé includes about 15 years at the aerospace and defense giant Boeing, echoed the comments of many House and Senate appropriators who have suggested part of the solution to the sequester’s “meat ax” cutbacks would be a return to regular appropriations bills.

“At some point in time, there needs to be some sort of reinstallation of regular order,” Hansen said. “It isn’t that we’re not going to have pain otherwise, but … nobody would make these kind of decisions this way.”

The FAA situation was somewhat unique, since the agency had much of its budget funded by trust funds not subject to the sequester. The money to pay the air-traffic controllers will come from other FAA programs, particularly unspent funds for airport improvements. But in a sign of the times, even organizations pushing the FAA carve-out were not entirely happy.

“At a time when we should be modernizing our infrastructure to improve efficiency, capacity and U.S. global competitiveness, sequestration-related issues should not be solved on the backs of airports,” the U.S. Travel Association said in a statement Friday. “We urge the Department of Transportation to do everything in its power to find appropriate savings to fund air traffic controllers and avoid transferring funds away from critical airport infrastructure.”