Republicans argue that the law will cause premiums to spike and that consumers should be more aware of its range of taxes on insurance companies and other healthcare players.
Democrats say the law will slow premium growth and ensure more care for every dollar. They argue that bills like Cornyn's give insurers a pretext for raising premiums by allowing them to blame ObamaCare.
Non-partisan experts say that healthcare reform will raise a small number of premiums, particularly in the individual insurance market, but lower many others.
Cornyn's Patients' Right to Know Act echoes House legislation introduced by Rep. Greg Walden (R-Ore.) in March.
Both measures require insurers to tell consumers the amount paid under the Affordable Care Act's exchange fees, risk-adjustment charges and other taxes.
Cornyn's bill also calls for the Government Accountability Office (GAO) to study how healthcare reform affects premium costs over time, and requires federal health officials to post the auditors' findings online.