No Surprise Bills for New Moms Act This bill amends health care plan provisions of the Public Health Service Act, the Employee Retirement Income Security Act of 1974 (ERISA), and the Internal Revenue Code to provide for enrollment of newborns in a health care plan for the first 30-day period after the newborn's date of birth and establish a uniform 60-day enrollment period thereafter. It would also require all health plans and insurers to notify parents of newborns if they receive a bill for a newborn who is not enrolled in a health insurance plan.