"Under a wrinkle that dates back to enactment of the law, members of Congress and thousands of their aides are required to get their coverage through new state-based markets known as insurance exchanges. But the law does not provide any obvious way for the federal government to continue paying its share of the premiums for the comprehensive coverage"
Like any true Democrat, Rep Waxman doesn't think they should be bothered by any actual law.
Representative Henry A. Waxman, a California Democrat who helped write the 2010 law, said, “The federal government, as our employer, should provide the same contributions it makes to our current health plans.”
HHS has made it very clear to the rest of us though that we dare not even consider such an arrangement.
"FAQS About Affordable Care Implementation (Part XI)” (FAQ) available here issued by the Departments of Labor, Health and Human Services (HHS), and the Treasury (collectively, the Agencies) on January 24, 2013 sends a clear message to employers that trying to escape ACA or other federal group health plan mandates by replacing their traditional insured or group health plans or policies with health reimbursement arrangements (HRAs) or other arrangements under which the employer agrees to provide a fixed defined contribution to be used to buy or reimburses employees for buying individual health insurance generally won’t pass legal muster. The FAQ also indicates that employers sponsoring HRAs that only reimburse medical expenses, not individual health insurance premiums also need to review their arrangements to verify that those programs also comply with ACA and other applicable rules." [emphasis added]
It has been prohibited to use Section 125 unreimbursed medical funds to reimburse insurance premiums. Outside those two mechanisms I'm not aware of any way to reimburse individuals for premiums and not run afoul of any other law. The one exception being giving them a raise and taking the tax it. Would love to see Congress pass out $10,000 raises to everyone and how that would go over.