White House officials strongly object to the notion that they’re going to sign on to a deficit deal that makes its main cuts in Medicaid. But they don’t deny, and in fact endorse the idea, that Medicaid will come in for some cuts. So I spent much of a day asking health-policy experts the same question: If you need to cut Medicaid, how would you do it?

One way is to simply cut spending on the program. That’s the approach you see in the Republican budget. Currently, the federal government contributes to Medicaid based on need. That means spending goes up if there’s, say, a massive financial crisis that knocks millions out of work. But Republicans want the federal government to tie those contributions to a formula that’s unrelated to need and, in fact, grows more slowly than health-care costs. And that would work. You can spend less by spending less. But it’d mean the program either needs to cut benefits for children, the very poor and the very old and disabled, or kick some of those people off Medicaid entirely. That is to say, it shifts costs rather than controlling them. And we need a better solution to Medicaid than simply “less of it.”

Indeed, one of Medicaid’s problems is that it is, if anything, too cheap. It pays doctors much less than private insurance or Medicare. The result? Doctors don’t like to take Medicaid patients. The New York Times reported Thursday on a study in which researchers called doctor’s offices to schedule appointments for children with conditions like “diabetes, seizures, uncontrolled asthma, a broken bone or severe depression.” When the researchers said the children were covered by private insurance, all but 11 percent got an appointment. When they said the children were covered by Medicaid, two-thirds didn’t get an appointment.

“In some cases,” says Len Nichols, director of the health-care policy program at George Mason University, “we would do better if Medicaid paid more. If we could get more doctors to treat the expectant mothers on the program and give them better care, that’d reduce the really expensive stuff from the neonatal intensive-care units. And when you look at that study in the Times, notice that the kids were waiting for specialists. That’s a disaster. If the primary care doctor has sent you to a specialist, that means you’ve got a problem they can’t solve. And if you have to wait, it festers.”

You don’t need to be a deficit hawk to worry when an 11-year-old’s seizures go untreated. But if you are a deficit hawk, you should be particularly worried. Continually sending the paramedics out is really, really expensive. Worse, it’s wasted money: A dollar spent keeping a kid healthy and learning is worth a lot more to our economy than a dollar spent stabilizing kids after they become unnecessarily sick.

Though sometimes better care costs more, at least upfront, sometimes it costs less. And the various experts I consulted believed there was one big opportunity for saving money in both Medicare and Medicaid: the “dual eligibles.”

These are the people who are so sick and so poor that they qualify for Medicare and Medicaid. Typically, Medicare might cover their hospital costs, but Medicaid will cover their long-term care. And they are really, seriously, no-joke expensive. They account for 40 percent of Medicaid’s spending even though they make up only 15 percent of its members, and if you add in Medicare’s spending, you’re looking at more than $200 billion a year for this group alone.

But expensive care isn’t necessarily good care. These people are often disabled and in no real shape to navigate multiple government and medical bureaucracies. There’s little coordination among their various doctors and hospitals and nursing homes. If their cases were managed better, they’d cost a lot less and the people would be a lot healthier.

The problem is that although coordinating their care could save us many billions over time, it’s hard to do. You can’t just tell the Congressional Budget Office you’re going to try really hard and expect it to score your efforts as reducing the deficit by $40 billion. Worse — at least from the perspective of budget negotiators looking for new savings — a lot of the best ideas were in the Affordable Care Act. The law even set up the Federal Coordinated Health Care Office to oversee the effort. That office, says Edwin Park, a Medicaid expert at the Center on Budget and Policy Priorities, “is now sending out grants to states to test new delivery system models for the dual eligibles.” So how soon can we expect to see some savings? Park doesn’t sugarcoat it. “This will take a number of years before we know exactly what models work.”

There are, of course, other places where we could plausibly eke out a few billion here or there. The administration says its budget proposal would save $100 billion over 10 years, and the costs would fall on drugmakers and providers rather than the disabled and the very poor. There was some skepticism among the experts I consulted as to the administration’s ability to achieve those savings, but in the long-run, whether they’d really get $60 billion or $100 billion is almost irrelevant.

Nothing that anyone has proposed will be sustainable if we can’t figure out a way to care for Medicaid and Medicare’s sickest patients in a most cost-effective way. Shifting costs won’t work because we’re too decent a nation to let these people die in the streets. Taxing providers or further lowering reimbursement rates might buy you some time, but the savings will either be eaten up by cost growth or, if you cut too deep, be turned into cost shifting, as we’re already seeing with the kids who can’t get an appointment. In the end, it’s really all about the tough, uncertain work of improving care, even if that work is hard for the CBO to score or the budget negotiators to tout. A serious commitment from both parties to work continuously and cooperatively on the dual-eligibles problem would be worth a lot more than the cuts and trims we’re likely to see.