The Trump administration’s top Medicare official blasted a plan by some Democrats to make the national health insurance program available for everyone, calling “Medicare for All” an “absolutely lousy idea.”

“The Medicare program is intended and designed for seniors, and we need to do everything that we can to strengthen the program for seniors,” Seema Verma, administrator of the Centers for Medicare & Medicaid Services, said Oct. 2.

Her comments come about a month before the November midterm elections as...