First of all, there aren't nearly as many as politicians on the right imply. Unless you live in a state that has expanded Medicaid, most "able bodied men" who get Medicaid benefits are either unemployable because of a disability of some kind or employed but still too poor to afford insurance, even on the "market" created by the Affordable Care Act. Weakening the ACA's expansion provision without completely axing a popular program is, I believe, the real reason Republicans are proposing "reform"; it has nothing to do with fraud, abuse, or the exploitation of the program by a massive but silent cabal of "able bodied men."
As someone who worked alongside the public mental health system for seven years in a non-expansion state, I do have a few thoughts on the matter of reform, though.
The "able bodied men" I worked with, almost to a man, wanted to work. Work is an incredibly important part of the male self-image in America, especially acute in the plains, south, and the midwest, states as "Red" as they come. But mental health disabilities, while often not precluding work, still create tremendous levels of discrimination by employers (100% of the time, in my experience), despite the existence of the Americans with Disabilities Act. The ADA, while a potentially powerful tool, essentially requires someone to self-disclose a disability, opening them up to being denied employment on other pretexts. In the mental health field in particular, men are encouraged to accept disability and disabled identities, to parrot back to providers their diagnoses as fundamental parts of themselves. It was routine to be introduced to someone by name and diagnosis, even though the work I was called to do was ostensibly based on recovery and moving beyond being identified as an illness.
By accepting the life of a mental patient, benefits and services—many of them quite helpful and valuable, such as housing and therapies—would be available to our ostensible "able bodied men." But this access also came with lifelong limitations, both from the system itself (more on those later) and within the minds of the men in the system. Despite wanting to work, these men often don't feel worthy of it, much less capable.
Once in the mental health system, 100% of them also become medicated. While many find these medications helpful, the meds often come with devastating side effects: lethargy; obesity; tardive dyskinesia, which weakens muscles and creates Parkinson's-like tremors. These medications can make the kind of work often open to those who want to work their way off the system, generally entry-level and labor intensive, all but impossible. And even if an "able bodied man" were to convince his service providers that he should seek alternative treatments, there are no guides for stepping down from psych meds, resulting in withdrawal syndromes that are often worse than the symptoms that led to the psychiatric diagnosis to begin with. Especially in rural areas, alternative therapies, such as talk therapies, are difficult to access or unavailable, so our supposed "able bodied man" is out of luck if he both wants help for his mental health challenges and an able body.
More generally, the entry-level work already mentioned that is available to those on Medicaid doesn't come with health insurance, doesn't pay well enough to purchase insurance via the ADA, is part time, and is dangerous or physically demanding. Kicking "able bodied men" off Medicaid will simply leave many of them impoverished, ill, and injured. With no other recourse, they will end up with unstable housing, inadequate nutrition, and frequent visits to the ER. This would shift costs from the public and onto private insurers, as these once "able bodied men" show up at hospitals with a mission to serve everyone regardless of ability to pay, therefore passing those costs along to those of us with private insurance coverage.
Thus an expensive public program becomes an even more expensive public problem, paid through ever-increasing health insurance costs for employers and the employees who qualify for benefits. Chances are that most Republican lawmakers haven't considered this, but it's possible many have but figure that the middle classes have just gotten used to paying more for insurance every year and won't make the connection to the Medicaid cuts they propose.
If we want to actually solve the problem, we should mandate a living wage and vastly expand Medicaid (or more properly Medicare, which, while flawed, is a much better system) to include everyone, much like every other industrialized nation has done. But, since obvious solutions are also politically radioactive in these United States, we could try these half-measures instead:
1. Emphasize preventative care. Private insurers are already starting to do this (though often poorly). While he is dreadfully wrong on many of the details, RFK, Jr. is right about this in the broad strokes. The system should pay out/subsidize prescriptions for nutritious foods, for example, which are often out of reach for those poor enough to qualify for Medicaid. Likewise for gym memberships, exercise equipment, and vouchers for safe and healthy housing. We're perpetuating the problem into infinity when kids of families that receive Medicaid are exposed to lead—whether that's through exposure to old paint or directly injected through the barrel of a gun.
2. Coordinate with other healthy living initiatives (and restore the ones the Trump administration has already killed). If we want to save public money in the long run, we need to spend it now cleaning up neighborhoods (and on lead abatement, as above), creating walkable cities, providing medical transportation in rural areas, and subsidizing neighborhood gardens.
3. Provide evidence-based alternative treatments. Plenty of talk and behavioral therapies have good evidence to back them, such as DBT, CBT, and exposure therapy (for PTSD). They're expensive at first but cheap in the long run. I'd rather pay for someone's equine therapy than see them debilitated by TD, if it comes to that. It makes little sense to have an environmentally damaging "all of the above" strategy for energy policies while not having a potentially helpful one for health care. Further, having more options is synergistic: better physical health leads to better mental health and makes people more employable, more "able bodied."
4. Create greater flexibility. Because so few entry level jobs provide benefits and are often hard on the bodies that do them, one should not have to face the binary choice of employment or benefits. A system designed to graduate benefit levels depending on income, availability of viable options on the ACA marketplace, and the healthcare needs of the individual could go a long way towards the every-"able bodied man"-employed vision of the political right.
The idea here goes beyond a safety net: if we want "able bodied men" to get off Medicaid and to "get back to work," we need a much more solid foundation from which they can launch.