The picture looks bleak for universal health insurance. Emboldened by their seizure of the House of Representatives last year, Republicans voted to repeal President Barack Obama’s health reforms, which at least brought us closer to covering everyone.

Around the country, meanwhile, GOP governors are suing to overturn the coming mandate that every American must obtain coverage. Republicans even tried to replace Medicare with a voucher plan not guaranteed to pay the full cost of coverage for seniors.

Given such developments, you may wonder if I have coverage for getting my head examined, because I’m convinced that some form of universal coverage is inevitable.

First, efforts to undo the Obama reforms will fail because when people get medical coverage, they won’t let it go. Consider the Republican Medicare proposal; near Buffalo, it helped tip a safe GOP House seat to the Democrats. And surprisingly, 60 percent of respondents in a recent Kaiser Family Foundation poll opposed GOP Medicaid plans as well.

So politicians may attack the Obama reforms, but who among them will now say insurers should be able to reject sick people? That young adults should be ineligible for coverage on their parents’ policies, especially at this time of high unemployment? That employers simply needn’t provide coverage? These stances will be political poison.

Second, big business understands the need for a universal plan. Wal-Mart and Intel, to cite two examples, have called for a system of affordable universal coverage — joining hands with a leading union in doing so.

Third, the states are leading us to the promised land by showing that universal coverage works — and people strongly support it. Since 1974, Hawaiians have enjoyed mandatory employer coverage, and now non-elderly islanders are half as likely to lack insurance as all such Americans. In Massachusetts, 98 percent are covered thanks to a 2006 insurance overhaul — under then-Gov. Mitt Romney, a Republican — that mandated everyone get coverage and provided aid for those who could not afford it.

And last week Vermont’s governor signed a bill putting the state on the road to a universal single-payer system. Note that this is pretty much how the Canadian system got started in the 1940s. A lone rural province, Saskatchewan, adopted single-payer universal coverage, and it was so popular that voters all over the country soon began clamoring for it.

Fourth, paying for health care is awfully tough without covering everyone. That’s counterintuitive, but universal coverage and cost control go together in every comparable country on Earth. You need healthy young people paying into the system, and unlike our current smoke-and-mirrors arrangement, in which cost-shifting obscures who’s paying what, everyone must understand that we all pay. Universal coverage paradoxically empowers — even forces — governments to set rates and clamp a lid on spending. That’s crucial, because we spend vastly more of our gross domestic product on health care than anyone else, and the rate of increase is crippling. Yet we rank worse on most measures of health and leave 50 million people uncovered.

Let’s not kid ourselves. Every modern country struggles to control health-care spending, with or without universal coverage. This is probably the Achilles heel of the Obama plan. But if it stands — and I’m betting on it — that part will come too, because we’ll have no choice.

Stricter cost controls are inevitable. Just like coverage for all.

Daniel Akst is a columnist for Newsday on Long Island, N.Y.