Obamacare Insurance Cost. It depends on the category of insurance you choose bronze, silver, gold, platinum. As metal rises so does coverage and price. However, within Obamacare, silver insurance is the most comprehensive, as it is prioritized by the government, and provides clients with up to 94 percent coverage. From zero dollars a month, you will find insurance that meets your needs. The Cost of Obamacare Insurance varies according to the financial information of each client.