Rep. Robert E. Andrews (D-N.J.), who played a key role in passing the health-care law and has worked on its implementation, said he told White House officials early this summer he had been hearing from insurers that the online system had flaws. “Nothing I told them ever surprised them,” Andrews said in an interview. “The White House has acknowledged all along something this massive was going to have implementation problems.” Two allies of the administration, both of whom spoke on the condition of anonymity because of the controversy surrounding the rollout, said they approached White House officials this year to...