WASHINGTON (Reuters) – The White House is coming under pressure from some of its closest allies on healthcare reform to name a chief executive to run its federal health insurance marketplace and allay the concerns of insurers after the rocky rollout of Obamacare.

Advocates have been quietly pushing the idea of a CEO who would set marketplace rules, coordinate with insurers and state regulators on the health plans offered for sale, supervise enrollment campaigns and oversee technology, according to several sources familiar with discussions between advocates and the Obama administration.

Supporters of the idea say it could help regain the trust of insurers and others whose confidence in the healthcare overhaul has been shaken by the technological woes that crippled the federal HealthCare.gov insurance shopping website and the flurry of sometimes-confusing administration rule changes that followed.

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