The major change relates to Obamacare subsidies. Those tax credits, which offset the cost of insurance premiums and out-of-pocket medical expenses, are available to low- and moderate-income people who enroll in Obamacare insurance.
Under the new fix, a person in the affected states must have begun an application on their Obamacare exchange, but still be waiting for a determination of their eligibility for subsidies to offset the cost of insurance premiums.
In properly functioning Obamacare exchanges, there is essentially no lag in making such eligibility determinations electronically, but in some states there is the "extraordinary" problem of a long, ongoing lag, the official said.
In affected states, a person who bought health insurance from a plan outside the exchange while awaiting their subsidy determination will receive subsidies if it turns out they are deemed eligible for the credits, according to the rule change.
(Read more: Obamacare hits 4 million sign-ups as bar lowers)
"CMS is committed to supporting state efforts to successfully implement their marketplaces," the agency said in a statement. "We recognize that some states have experienced difficulties in processing automated eligibility determinations and enrollments, and today we released guidance providing options to marketplaces to ensure eligible consumers have access to financial assistance and issuers are paid."
"We will continue to work closely with states to assist them in moving forward with their marketplaces so that all consumers can take advantage of their new coverage options."
U.S. House Energy and Commerce Health Subcommittee Chairman Joe Pitts, R-Pa., blasted the rule change, which is just the latest in a series of fixes, loosened regulations and time extensions that the Obama administration has implemented in connection with the rollout of the Affordable Care Act.
"It is outrageous for the Obama administration to be quietly telling states: pay subsidies now, worry about the paperwork later. The administration is blatantly ignoring the law, paying subsidies to plans outside of exchanges," Pitts said.
"Additionally, this 'pay now, verify later' directive could be a boon for fraudsters, raising the administration's unaccountability to the likes we have not seen. Once again, the self-proclaimed 'most transparent administration in history' is caught trying to hide another change from the public. The unilateral delays and changes have been rampant. The American people deserve better—they deserve fairness for all."
—By CNBC's Dan Mangan. Follow him on Twitter