WASHINGTON (Reuters) Jan 03 - U.S. officials on Thursday gave four states currently governed by Republicans the green light to set up their own health insurance exchanges under President Barack Obama's healthcare reform law, an initiative largely opposed by Republicans. The U.S. Department of Health and Human Services said Idaho, Nevada, New Mexico and Utah joined a list totaling 17 states and the District of Columbia that have all won conditional approval to establish their own state exchanges, with operations set to begin on January 1, 2014. A fifth Republican-governed state, Mississippi, applied to operate a state exchange, but has not received approval because of a dispute about how much authority state officials should exercise over the operations of its prospective online marketplace, officials said. The U.S. administration also cleared an exchange that Arkansas plans to run in partnership with the federal government. Delaware received approval for a similar partners...