Cover Outstanding Vulnerable Expansion-eligible Residents Now Act or the COVER Now Act This bill establishes a demonstration program to allow local governments to provide health benefits to the Medicaid expansion population in states that have not expanded Medicaid. Under the program, local governments may provide coverage for individuals who are newly eligible for Medicaid under the Patient Protection and Affordable Care Act (i.e., the Medicaid expansion population) for a maximum of 10 years, or until their respective states expand Medicaid. The bill provides a 100% federal matching rate for the first three years of program participation. The bill prohibits states from taking certain actions against participating localities, such as withholding funding, increasing taxes, or restricting provider participation. States that violate these requirements are subject to certain funding penalties.