The IRS is already the administrator of the second-largest anti-poverty program in America. It's about to become the second-largest health regulatory agency in the Federal Government, since they'll be in charge of lots of rules governing who does and doesn't count as a "full time employee" for insurance mandate purposes, computing insurance subsidies for middle class households, monitoring employer-sponsored insurance plans, and so forth. As they ramp up for 2014, they've started issuing hypotheticals estimating the price family insurance plans. One of these hypotheticals assumes that a family of four will end up spending $20,000 on their insurance policy. This is far more than most households can expect to spend. In reality, a family that sized earning less than 400% of the Federal Poverty Line, or $92,200 in 2012, will pay somewhere between $100 and $750 per month for health insurance. That's a big bite -- equal to a car or student loan payment in many cases -- but it's something that households can probably manage.
Once again, I've reproduced the incredibly helpful table from the Vermont Health Care Reform Agency of Administration. The UC Berkeley Labor Center also has an Affordable Care Act calculator that might be useful.