This is a US-specific version of the emergency medical care for immigrants objection to immigration. The broad outline of the argument (in the US context) is as follows:

• Many immigrants, particularly illegal immigrants lack health insurance and lack the financial resources to pay for their own health care.
• As a result, when they need to avail of health care, they typically do so using emergency medical care provisions in hospitals. Emergency care units are bound by law and ethics not to turn away patients, regardless of their willingness or ability to pay.
• While the most direct brunt of the costs is borne by hospitals, the costs are passed on to the general population in two ways: (i) as taxpayers, they fund the goverment subsidies to the hospitals, (ii) the increased costs of operation may be passed on to insurance companies and hence to insurance purchasers in the form of higher premiums.

Blog posts and articles making this case

• Transcript of “The Elephant in the Room: Panel on Immigration’s Impact on Health Care Reform”, a panel conducted by the Center for Immigration Studies.
• Obamacare Loopholes May Benefit Illegals at Taxpayer Expense by James R. Edwards Jr., May 8, 2012, on the website of the Center for Immigration Studies.
• Memo From Mexico | Why Mexican Hospital Emergency Rooms Aren’t Swamped by Allan Wall, February 19, 2007, for VDARE.
• Health Cost Study Likely to Disregard Immigrant Impact, letter to the editor, February 5, 2003, for VDARE.

Quote from Krikorian’s book making this case

Below is a lengthy quote from a book by Mark Krikorian that elaborates on the problem of emergency medical care.

The cost to taxpayers of the Medicaid program is obvious, but immigrants without any insurance at all also impose significant costs on government and on consumers. After all, even the uninsured get sick, and no modern society is going to allow them to go entirely without treatment. This treatment usually happens at emergency rooms; in the words of one recent study, emergency rooms “have become one of the nation’s principal sources of care for patients with limited access to other providers, including the 45 million uninsured Americans.”19 (Actually, as we’ve seen, a large portion of the uninsured are noncitizens, rather than Americans.) Taxpayers bear some of the costs incurred by the emergency departments of these “safety net” hospitals. Medicaid sends “disproportionate share hospital” payments to hospitals serving the poor, including immigrants; and in the Medicare prescription drug bill, Congress allotted payments of $250 million per year (for four years, through 2008) to the states for treatment provided to illegal aliens.20 In addition, “A number of states also provide additional support to emergency and trauma systems through general revenues or special taxes.”21 In California, where households headed by immigrants (legal and illegal) make up the majority of the uninsured,22 emergency departments statewide lost nearly half a billion dollars in 2001-2002, up 58 percent from just two years before.23 In Texas, where immigrant households account for nearly four in ten of the uninsured, the state’s twenty-one trauma centers lost $181 million in 2001 due to unreimbursed costs. There is no estimate of total health-care costs borne by taxpayers due to immigration overall, but there are a number of estimates regarding just illegal aliens, who represent about one third of the foreign-born population. One estimate of the cost to emergency providers of treating illegal aliens is $1.45 billion, and the cost to counties along the Mexican border nearly a quarter of a billion dollars.24 Other state-specific estimates: nearly $600 million in uncompensated care for illegals provided by New York taxpayers in 2006;25 in Florida in 2005, $165 million;26 in Texas in 2004, $520 million;27 in California in 2004, more than $1.4 billion;28 and in Arizona in 2004, $400 million.29 These estimates do not include the costs of care provided to uninsured legal immigrants—an important point, since the main reason for immigrant poverty, and thus the lack of health insurance, is lack of education, not legal status.30 But not all uncompensated care is covered by government, and hospitals must thus write off a portion of the costs of treating the uninsured. Hospitals then shift these costs onto paying patients and their insurance carriers, resulting in higher premiums for those who do have health insurance. One report estimated that each American family with insurance through a private-sector employer paid more than nine hundred dollars extra in premiums in 2005 due to the cost of treating the uninsured.31 The Emergency Medical Treatment and Active Labor Act (EMTALA) requires all emergency rooms nationwide to screen and stabilize any and all comers, whether they can afford it or not—so when hospitals can no longer shift enough of the costs for uncompensated care to others, they simply close their emergency rooms. This doesn’t create a direct monetary cost for consumers, but it does hold the potential to levy the ultimate tax—death—on Americans in need of emergency care. From 1993 to 2003, the number of hospitals with emergency rooms declined by 9 percent, even though the number of emergency room visits increased 26 percent, double the rate of increase in the population.32 In Los Angeles, more than sixty hospitals have closed their emergency rooms over the past decade.33 A 2005 report bleakly summarized the situation: “To the degree that immigration continues to increase, it is likely that the uninsured will also continue to increase as a proportion of the population.”34

Krikorian, Mark (2008-07-03). The New Case Against Immigration: Both Legal and Illegal (pp. 173-175). Penguin Group. Kindle Edition.