"The problem with his statement is that rights aren't the government's to give. John Locke, the 17th century English philosopher, wrote about inalienable rights: God-given rights that can't be taken away."
The most obvious way the government could provide health care is for a fully socialized, single-payer government provided health care system--the kind that Bernie Sanders desires. Such a system would be a disaster. With the broken system we have now, the number one purchaser of medical services already is the government. The primary reason health care services are so expensive is that there is very little profit and loss calculation undertaken by anyone because the third-party-payer system drives a wedge between the demander of medical services (the patient) and the supplier of the services (the doctor and/or hospital). Sanders' proposal (and all single payers systems like it) drives the wedge even deeper and farther.
Additionally, any claims that, under a plan such as Sanders desires, we'll all be more healthy would be laughable if the issue were not so serious. What Sanders' plan will do is increase the demand for medical services, but it will not increase supply, so we should expect the same sort of shortages they experience in Great Britain's National Health Service. On the issue of government intervention in the health care industry, I highly recommend Colin Gunn's film Wait Till Its Free.