Connecticut has been so successful in getting people to sign up for health insurance through its online marketplace that it is setting up a consulting business to help other states build and operate websites where people can compare and buy private insurance policies. And the Obama administration has encouraged the effort, in the hope that more states will run their own exchanges in 2015 or 2016. Kevin J. Counihan, the chief executive of the Connecticut exchange, said Monday that it would license or franchise its technology, selling an “exchange in a box” to other states. It would offer a package of basic services, with an option for states to buy more. “We have something that’s working, and we want to share it,” said Lt. Gov. Nancy Wyman, who is chairwoman of the board of the state exchange, Access Health CT.