Tax Exempt Hospitals Responsibility Act of 2006 - Amends the Internal Revenue Code to: (1) deny a tax exemption to medical care providers (i.e., tax-exempt charitable or teaching hospitals) that fail to adopt and carry out policies for providing medically necessary care to low-income individuals without health insurance; (2) deny a tax deduction for contributions to such providers; and (3) impose excise tax penalties on such medical care providers for failing to provide medically necessary care to low-income uninsured individuals, for overcharging for such care, and for failing to make certain disclosures to patients and the public relating to medical care and pricing.