"Big Brother" rumors (often linked to the "mark of the beast" referenced in Revelation 13:16-18) warning that the government will ultimately require all citizens to be implanted with microchips have been around just about as long as microchips have, and specific claims that health care reform legislation will require such implantations date to the Clinton administration. So, the warning reproduced above — that health care reform legislation passed by the U.S. Congress in 2010 would require "this sort of device be implanted in the majority of people who opt to become covered by the public health care option" — is nothing new under the sun. This warning is also just as false as all such previous rumors, a combination of someone's using inapplicable source material and also misunderstanding the meaning of the information contained within that source.
First off, the referenced information was not part of the "Obamacare" health care legislation actually enacted by Congress. The page numbers and language cited in the example above were taken from HR 3200, an early House version of health care reform legislation which was never passed by Congress; passages cited from HR 3200 are therefore irrelevant. The cited wording did not appear in the replacement bill (HR 3590) eventually passed as the Patient Protection and Affordable Care Act, and although similar language was included in initial versions of the subsequent reconciliation bill (HR 4872), it too did not appear in the final version of that bill as passed by Congress.
Second, nothing in any of those unpassed bills mandated that anyone be implanted with any type of microchip or RFID-based device, for any reason. The passages quoted above reference a section of the legislation that simply called for the creation of a registry which would allow the Department of Health and Human Services to collect data about medical devices "used in or on a patient" (such as pacemakers or hip replacements) for purposes that included tracking the effectiveness of such devices and facilitating the distribution of manufacturer recall notices. Absolutely nothing in those bills required that patients receive any type of implantable device (microchip or otherwise) or authorized the government to mandate the implantation of devices in patients.
Some May 2012 versions of the hoax circulated by e-mail and Facebook postings displayed a photograph of the purported chip meant to be implanted, an item described as the size of "a grain of rice." The chip shown in the photo is actually one that measures glucose levels in diabetes patients, as evidenced by this 2007 article about this new concept in glucose monitoring.
Updates: A July 28, 2013, article about implanted microchips being "given a test run on the proud and patriotic citizens of Hanna, Wyoming" was mistaken by many readers for a genuine news story. However, that article was just a spoof from the satirical National Report web site.
The rumors made another appearance in the fall of 2016, when various stories began to appear once again about RFID chip implantations, this time mandatory as of 2017 rather than 2013. Needless to say, these rumors were also completely false.