No. No such law currently exists at either the state or federal level. However, liability insurance bills have been introduced in California, Massachusetts, Connecticut, New York, Pennsylvania, and Maryland as part of larger gun control packages.
Congress, notably, has not said it would consider mandatory gun insurance. Though President Obama has advocated for “common sense gun safety measures,” he also has not proposed such legislation.
At the state level, Massachusetts state Rep. David Linsky (D) is an outspoken champion of mandatory gun insurance laws and is pushing the legislation in his state. Gov. Dannel Malloy (D) of Connecticut has asked state officials to study the efficacy of such a measure.