When someone shows up at an emergency room, the hospital treats them whether or not they can pay. Since sometimes they can't pay, that imposes costs on hospitals. And many people think that those costs translate into higher prices for insured parents. Annie Lowrey discusses this in terms of Medicaid expansion:
Second, financing care for the uninsured forces hospitals and doctors to charge the insured higher prices, meaning higher premiums for coverage. (Economists call this a “cost shift.”) “Health insurance reform would reduce this ‘hidden tax’ that individuals with private health insurance pay for uncompensated care for the uninsured,” the C.E.A. report argues. State and local governments would benefit by having to pay less to cover their employees.
You also sometimes hear the related argument that Medicare's relatively low reimbursement rates cause "cost-shifting" onto the shoulders of private insurance plans. But neither story makes a ton of sense to me. Think about the CVS downstairs from my office. It charges prices that it believes are profit-maximizing. Now suppose some indigent person comes in and burns all the magazines on their magazine rack for fun. The guy's got no money, so CVS can't recoup its losses. Does this force CVS to raise prices on Diet Coke to make up for the cost? No—CVS was already charging profit-maximizing prices, and past losses are irrelevant to determining optimal forward-looking pricing strategy.
Now you could say that if hospitals were allowed to refuse to treat the uninsured, then there would be more excess capacity in the hospital system, which would reduce the profit-maximizing price to charge for some services. But the proposal on the table isn't to let more people die, it's to give more people health insurance. Common sense says that will reduce the slack supply in the health care system and at the margin raise prices.
That's why even though in the short-term I think the politics of Medicaid expansion will be driven by idiosyncratic features of whomever happens to be governor today, the longer-term issue looks different. States with plenty of health care providers will be hungry for the federal dollars, but states (primarily on the Plains) that already spend a great deal of time worrying that they don't have enough medical personnel will have a more serious long-term concern.