This Politifact.com page examines a similar claim made by Michelle Bachmann. It gives her claim their worst rating: "Pants on Fire". Bachmann claimed that the government was going to be collecting intimate details about people as a result of Obamacare, and in fact, the government is not. This claim is a misinterpretation of a "Hub" that the government is creating, which will allow appropriate government agencies to look up data _that it already has_.
This Politico page discusses claims that Obamacare would expose your medical tests and other medical data to the government. The government would access and request some data indicating eligibility for subsidies, but, as you can see from this Obamacare application form, no medical information is requested.
The notion that the Affordable Care Act will expose sensitive data to the government appears to be nothing but a hyperbolic misinterpretation.