In proposing the idea, the insurers said a bypass giving them direct access to the federal platform that determines a consumer’s eligibility for a subsidy would alleviate the traffic on the website, healthcare.gov, and provide more breathing room to fix complicated technical problems that threaten to persist beyond a crucial, self-imposed Dec. 1 deadline.

But even if such a shortcut could be designed, federal officials are concerned about protecting personal data, such as confidential financial and tax information and immigration status. The security and privacy issues are likely to overshadow any possible compromise, according to people briefed on the discussions.

A more likely solution is for consumers to be able to work directly with an insurer to estimate their qualifications for a subsidy, leaving federal verification to a later date, some insurers said. Insurance executives declined to speak on the record because of company policies and concerns about alienating political officials.

Time is running out.