Senior citizens offering cookies and coffee are hard to reject. At least, that’s what supporters of insurance companies that cover people in Medicare are hoping. Recently, insurance-industry lobbyists brought people enrolled in private Medicare plans to Capitol Hill with a food truck, gave them red aprons to wear and asked them to talk about why Medicare should not cut payments to the insurers.

The insurance plans, known as Medicare Advantage, face a potential 0.95 percent rate cut in 2016 from the Centers for Medicare and Medicaid Services. The agency said because of the way insurers are paid by Medicare, most plans will actually come away with an average 1.05 percent increase in their payments next year. But insurance companies are lobbying hard to persuade Medicare officials to give them more. The CMS officials will announce their decision on April 6.

The annual exercise gets attention from lawmakers even though they do not directly control what Medicare officials decide, unless Congress were to pass a bill. This year, Speaker John A. Boehner of Ohio and Senate Majority Leader Mitch McConnell of Kentucky joined GOP committee chairmen from both chambers in a letter to the CMS protesting the cuts.

The argument puts Republicans in the odd philosophical position of arguing for higher Medicare entitlement spending.

The federal government spends more on people who are in Medicare Advantage plans than it does on people in the original fee-for-service Medicare program, where patients do not have a list of doctors that are in their networks but can see any medical provider that accepts Medicare. Those higher payments are part of the rationale behind the proposed cuts.

Before the health care law (PL 111-148, PL 111-152) passed in 2010, the private Medicare Advantage plans were paid 14 percent more per patient than Medicare spent on fee-for-service patients. The law called for gradual reductions to equalize the spending.

The Medicare Payment Advisory Commission said that after accounting for differences in the way Medicare Advantage plans report how sick patients are, which affects their payments, Medicare will pay the plans 5 percent more in 2015 for the beneficiaries than if those people stayed in fee-for-service Medicare.

Extra Spending for Advantage

Health plan industry officials used to say they could actually save Medicare money. During the Clinton administration, insurance officials said they could deliver better care than fee-for-service Medicare at lower cost.

The extra spending on Medicare Advantage in 2015 translates into $8 billion, more than four times what the National Institutes of Health spends each year on heart disease research, the top cause of death among Americans.

Advocates for the companies said the plans do a better job of coordinating patients’ care. In other words, the extra drain on the Medicare program is worth it because the plans are better at helping consumers stay healthy.

The private plan program “is the bridge to the future,” said Doug Holtz-Eakin, a former Congressional Budget Office director who leads an advocacy group seeking to block cuts in Medicare Advantage.

“Everyone knows we want a system permeated with coordination, care management [and] a home for the patient,” Holtz-Eakin said, adding that the plans offer the best opportunity for that type of care so far. “We pay plans more for that, and I would say, ‘Fine, because that’s the best value in the system.’ … What matters is what you’re getting for your spending.”

But the idea private plans are keeping their customers healthier doesn’t fit with what MedPAC found out about what plans say about the health of their patients.

One reason the plans are paid more is because industry officials tell Medicare their patients are more sick. Medicare offers higher payments if patients have medical problems. For every year a consumer stays in a Medicare Advantage plan, the health of the average patient in a plan is reported to be increasingly worse than for people who stay in fee-for- service Medicare, MedPAC discovered. It’s unclear why the health of patients in plans would be deteriorating faster than people who are in fee-for-service Medicare.

The industry’s lobbying effort, led by the trade association America’s Health Insurance Plans, has worked in the past. For at least the past four years, the CMS has proposed steeper cuts than they ended up finalizing. In 2013, CMS officials turned their proposed cut into an increase by changing their assumptions about whether Congress would block reductions in doctors’ pay.

Although Democrats imposed cuts in the health care law, Republicans are backed in their efforts to stop the cuts by Democrats in states such as New York, Minnesota and Oregon, where a large number of people are in Medicare Advantage plans.

Take It Out Back

Lawmakers say managed-care plans are part of the effort to move Medicare away from paying doctors and other health care providers on a piecemeal basis for every test and procedure a patient receives. They say that kind of fee-for-service payment system can lead to medical errors or unnecessary tests and treatments. Sen. Ron Wyden of Oregon, the top Democrat on the Senate Finance Committee, called the traditional program “outdated, clunky, fee-for-service, silo-driven” care.

“What we need to do is take fee-for-service medicine outside in the back and just give it a dignified burial,” he said. “There’s nothing else I know of that drives inefficiency in such a profound way.”

A number of lawmakers are trying to influence Medicare officials’ decision. In February, 53 senators, including 36 Republicans and 17 Democrats, wrote to the CMS urging it to curb the reductions. In the House, 239 lawmakers wrote to CMS acting Administrator Andrew Slavitt on March 12 “to strongly urge you to protect Medicare beneficiaries by reversing the proposed payment cuts” next month.

“The newly proposed cuts could represent a significant threat to the health and financial security of seniors in our congressional districts who rely on their MA plans to meet their health care needs,” said the House letter, signed by 174 Republicans and 65 Democrats.

“The overwhelming, bipartisan support sends a strong message to Medicare Advantage beneficiaries that members of Congress are standing up to protect their coverage,” said AHIP President and CEO Karen Ignagni, whose organization’s Coalition for Medicare Choices is encouraging 1.8 million seniors connected with the group to call and write lawmakers to protest the cuts.

Ignagni’s group was behind the coffee and cookie trucks. The logo for the campaign is “Protecting Our Life’s Sweetest Things.”

An earlier version of this article misidentified MedPAC as a political action committee.