Nonprofit health-insurance cooperatives are gaining favor among lawmakers working to revamp the U.S. healthcare system, but whether these entities could rein in prices by competing with private insurers is unclear. The idea represents a compromise on one of the most contentious points in trying to craft a bipartisan bill. President Obama is pushing for a government-run health-insurance plan that would compete with private insurers as a way to help extend coverage to 45 million uninsured Americans, but most Republicans and some moderate Democrats counter that the government's cost advantage would unfairly upend the private market.