Obamacare’s days are numbered. That was the message of the executive order President Donald Trump signed Friday, instructing government agencies to “minimize the unwarranted economic and regulatory burdens of the [Affordable Care Act].”

When I spoke with a handful of Trump supporters after the inauguration Friday, they said they eagerly awaited Obamacare’s end. Tanya, a woman from Virginia who was rolling a walker down I Street to the inaugural parade, said she was struggling with her $6,750 deductible. “As a business person who is self-employed, it’s killing me,” she said.

Nearby, Marlita Gogan, from Houston, said she just wants Trump to “do what he says”—repeal and replace Obamacare. Her daughter’s insurance premium has risen from $250 to $375, with a $5,000 deductible. “It’s too much,” she said. “You can’t even use it.”

But what’s less clear is whether the crown jewel of most of the Republicans’ replacements for Obamacare—health savings accounts—will ease the financial strain some people feel under Obamacare. The idea of these accounts is that people will sock away money, in some cases with the help of a government subsidy, to pay for their health care. Typically, they will simultaneously enroll in an insurance plan with a large deductible. The amounts will vary depending on the whims of the insurance market, but past studies of firms with HSAs have used a deductible of about $4,300 for a family, with a $1,300 employer contribution to the HSA. The high deductible would encourage them to compare prices among different doctors and find the cheapest one, while the savings account would, theoretically, allow them to store money to cover their planned medical expenses.

The Republican Study Committee’s recently unveiled plan calls for the “Enhancement of Health Savings Accounts.” The one proposed by Senators Bill Cassidy and Susan Collins would help states create HSAs for low-income adults. House Speaker Paul Ryan’s “Better Way” plan touts “Health Savings Accounts” as one of the “four major successful health reforms” of the 21st century, and says that “improving the flexibility of health savings accounts and other consumer-oriented health care options will further enhance individual choice.”

The plan put out by Representative Tom Price, a Georgia Republican and Trump’s choice to lead the Department of Health and Human Services, provides for the creation of high-risk pools that “offer at least the option of one or more high-deductible plan options.” These high-deductible plans would then be paired with a health savings account, where people can save money before taxes to pay for their medical care.

Health-savings accounts are already available in some insurance markets. Writing in Health Affairs, Timothy Jost explains how they would change under the various GOP replacement plans:

Replacement proposals would generally increase the amount that could be deposited in HSAs, make them available for more government programs, and otherwise liberalize program requirements. Some would even offer tax credits to partially fund HSAs. Supporters of HSAs argue that they reduce health care expenditures: When people spend money from HSAs they are effectively spending their own money rather than an insurer’s money; they will spend less and shop around to find lower-cost, and perhaps higher-quality, care.

The thinking is that forcing people to reckon with the true cost of medical procedures is our only hope in controlling health-care costs. “Medical prices are so distant from consumers that there’s no way we’re going to get costs under control,” said Steve Parente, a professor at the University of Minnesota who has analyzed Better Way and other conservative health-care proposals. “HSAs are not a perfect mechanism to get you there, but it’s a nudge.”

By way of example, he explained that he saved several hundred dollars on a prescription drug because he heard from someone that a Costco in town had the medication for dirt cheap. While this kind of bargain-hunting isn’t possible in emergencies, but having a high-deductible plan might prompt you to press your surgeon on just how much that shoulder operation is going to cost, he says. Parente said ideally, these high-deductible plans could be “bespoke”—tailored to someone’s medical conditions, so that, say, allergy shots could be covered before the deductible for someone with hay fever. Yes, he acknowledges, it might be painful at first to spend your own money on medical care; high deductibles are a major reason for American’s dissatisfaction with their health plans. People on high-deductible plans tend to go through stages of grief: “First, they’re like, ‘this is screwing us,’ then they get hardened, but then they survive it,” he said.

The push for high-deductible plans is part of conservative policymakers’ fondness for “consumer-driven” healthcare, says Renee Hsia, director of health-policy studies at the University of California in San Francisco, “where we see patients as empowered shoppers who can and should be making decisions about their health care with their wallet.”

But according to Hsia, the problem is that health care doesn’t work like most other consumer goods. “For example, if I want to go buy a loaf of bread, I can easily see the ingredients, I can look at the nutritional information, I can look at the price, and I know the consequences of buying the loaf of bread and not buying the loaf of bread (i.e., it either means having it or not),” she explained. “If I have chest pain, there is no much information I don’t have: I don’t know what the diagnosis is, I don’t know what it will require if I do see a doctor to get to a diagnosis and what tests I will require, I don’t know the consequences of not getting treated are, I don’t know what procedures I will require even once I do get to a diagnosis.”

Multiple studies have shown that the amount different hospitals charge for the same tests can vary by thousands of dollars. That’s the kind of thing a consumer could “shop around” for, in theory—but not if there’s only one hospital in town. And past studies have shown that hospitals are more forthcoming with the price of their parking lots than they are about the prices for routine tests.

What’s more, several of the Trump supporters I’ve interviewed, including Tanya, say they want to be able to keep seeing their favorite doctors. That might not be an option if they’re forced to seek out the one that’s cheapest.

High-deductible health plans do cause people to spend less money on medical care—by about 5 to 7 percent. They especially avoid things like getting lab tests and filling their prescriptions, particularly in the first year they have the plan.

That’s because it takes a while for money to build up in the health-savings account, and also, there’s a “newness factor,” said Anthony Lo Sasso, a health-policy professor at the University of Illinois. “There’s a learning curve, and that probably tamped down spending.

They also become more careful about going to the doctor. “You might give that upper-respiratory infection a few more days,” Lo Sasso said.

But the intended effect—that people will learn to shop around for the cheapest doctor—doesn’t always kick in. A 2015 study of a firm that switched to a high-deductible health plan found that the employees didn’t learn to price-shop after two years. Instead, they just reduced the amount of medical services they received, including potentially valuable services like preventive care. People with chronic conditions delayed care for themselves and their children. This is a recurring issue with high-deductible health plans, according to Paul Fronstin, an economist at the Employee Benefit Research Institute who led a study of a large employer who adopted a high-deductible plan. People don’t know that certain services—like, say, flu shots—are excluded from the deductible. Or, they worry that while they’re at the (covered) appointment, the doctor will find a potentially-cancerous lump, which would then compel them to get a scan that’s not covered before their deductible. That suggests people on high-deductible plans are getting less care, not just cheaper care.

Another question is whether people will be able to figure out how much they need to contribute to their health-savings accounts to offset their deductibles, or to parse which tests and procedures are skippable, and which aren’t. Insurance is already a domain that few Americans understand perfectly.

“If people don’t understand the cost-sharing of insurance, one should have very little hope that people are going to understand how they are going to take up and enroll in an HSA, and how to offset the burden of the high-deductible plan,” said Saurabh Bhargava, a behavioral economist at Carnegie Mellon University.

Finally, many economists doubt that most working-class Americans have enough spare money to put in their health-savings accounts to compensate for these high deductibles. Nearly half of Americans would have trouble scraping together $400. And because health-savings accounts shelter money from taxes, they tend to favor the rich, whose taxes are higher.

The tax credit Price proposes doesn’t increase at lower income levels like Obamacare’s subsidies, which might mean low- and middle-income people will continue to be squeezed by high deductibles.

Sara Rosenbaum, a professor of health policy at George Washington University, took the dimmest view of the GOP’s plans. She called health-savings accounts “a device that wealthy people can use to sock away pre-tax outcome to partially offset out-of-pocket costs for the health care [they] can afford to get.”

“It’s a nonstarter for people with low incomes,” she added.