Faced with withering criticism, CMS officials are asking for ideas on how to design a new payment system for treating Medicare patients who need only a day or so in the hospital.

The issue has turned into an administrative mess for the CMS, with billions of Medicare dollars at stake flowing to thousands of hospitals and doctors. Last October, Medicare implemented a new rule to clarify that patients needed two nights in the hospital to qualify for inpatient-hospital rates, but that so-called "two-midnight" rule has become more controversial than the old system...