Section 431(a) of the bill says that the IRS must divulge taxpayer identity information, including the filing status, the modified adjusted gross income, the number of dependents, and "other information as is prescribed by" regulation. That information will be provided to the new Health Choices Commissioner and state health programs and used to determine who qualifies for "affordability credits."
Section 1801(a) says that the Social Security Administration can obtain tax return data on anyone who may be eligible for a "low-income prescription drug subsidy" but has not applied for it.
What the bill doesn't contain is any limits on what is to be provided and penalties if your information is made public by government officials. This has obvious implications for both privacy and ease of identity theft.