Health and Human Services Secretary Tom Price made a bold promise during a Sunday morning interview with Meet the Press. “Nobody will be worse off financially” under the Republicans’ new health care plan, he boasted.

Let’s be clear: This is a lie. Price is making an impossible promise. Low-income Americans would receive significantly less help to purchase private coverage on the individual market under the Republican plan in Congress right now. The plan would also end Medicaid expansion in two years, forcing many even lower-income Americans to lose health coverage.

There is nothing in the plan to suggest those low-income Americans would suddenly gain cheaper — or even comparable — coverage to make up for what they lose.

The Trump administration is falling into a trap that bedeviled the Obama administration. Officials are pretending that health policy doesn’t have trade-offs, that they have finally written a plan that is great for everyone.

They are wrong.

Every health bill has people who do better because of its changes, and every bill has people who do worse. Change the system so one group pays less, and another group, inevitably, has to pay more — either through higher premiums, higher taxes (now or in the future), or higher out-of-pocket medical spending. Policies that benefit the sick can disadvantage the healthy; plans that give more help to middle-income Americans reduce the help that the poorest Americans get.

Here is how former Congressional Budget Office director Doug Elmendorf put it to me a few months ago. “Those trade-offs have bedeviled efforts to expand health insurance coverage for decades,” he said. “It is very hard to maximize health coverage while minimizing the cost to the government and disruptions to current insurance arrangements.”

Presidential administrations like to talk about the good things their health care plans will do. They make promises about how great it will be when a given bill passes. And that’s fine: Both Obamacare and the GOP plan make health care work better for certain groups.

But the White House can often go too far — promising that everyone will be better under the new system — and eventually, they must live with the consequences of making promises that are impossible to keep.

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Obama fell into the same trap as Price when he promised everyone can keep their plans if they like them

Remember when President Obama repeatedly promised that everyone who liked their health insurance could keep it? He made this promise dozens of time in the lead up to Obamacare’s coverage expansion.

He couldn’t keep it. Obama couldn’t build a health insurance market that guaranteed everyone could keep their coverage. His administration banned skimpy health insurance products that don’t cover things like maternity care or mental health services. The White House decided it was good policy to make sure all health coverage is comprehensive.

People who wanted comprehensive health plans won — and people who liked their skimpier, less expensive health plans lost. They were furious when they received cancellation notices in the mail. PolitiFact ultimately rated President Obama’s “if you like your health plan, you can keep it” promise as their 2013 lie of the year.

The Republican plan will leave some people financially better — and a lot of people financially worse

Price is falling into the exact same trap. He wants to say the Republican health care plan is great news for everyone. And there are undeniably people who do better under the GOP plan.

For example: Right now, Americans who earn more than $48,000 get no help to purchase health plans on the individual market. That has put coverage out of reach for some middle-class Americans. A lot of these people aren’t rich; last fall I talked to a PhD student who fell into this category and struggling to afford coverage.

Price’s plan would benefit people like this: It would give tax credits to all Americans who earn up to $75,000 — meaning someone like that PhD student would all of a sudden get help purchasing her coverage.

The Republican plan has its beneficiaries — but it also has losers, and lots of them. Low-income Americans would get way less help purchasing coverage under AHCA.

Take a 40-year-old in Juneau, Alaska, who earns $30,000 (whose situation you can explore through this very helpful Kaiser Family Foundation calculator). Right now that person gets an $11,200 tax credit to purchase health insurance on the individual market (mostly because health insurance is really expensive in Alaska, a rural state with few hospitals).

Under the Republican plan, that person would get just $3,000 — a 74 percent decline in their tax credit. There is no way that person will be financially better off under the Republican plan, unless the plan also manages to reduce the cost of medical care in Alaska by three-quarters. There’s nothing in the bill that could possibly accomplish that.

Medicaid enrollees have even more to lose. The Republican plan would end the Medicaid expansion in 2020, forcing those who benefited from the expansion to buy coverage on the individual market. Research from the Urban Institute suggests most of those people would not be able to afford a comprehensive health plan using just that tax credit — and, given that these people earn less than $15,000, they don’t have much extra money to spend on coverage.

Republicans have their reasons for helping someone like the PhD student I talked to — and hurting a low-income person in Alaska. They generally want the government less involved in providing health coverage and oppose income-testing any help that people do get. They prefer the idea of giving everyone the exact same amount of subsidy because it’s simpler and doesn’t disincentivize work.

Price can make promises like this one right now with few consequences. The AHCA has not yet passed Congress and we don’t know if it ever will. But if the Republican plan becomes law, that will lay the trade-offs bare, just as happened with Obamacare. People will lose under the law, and they will be angry that the Trump administration sold them a false bill of goods.