Tufts Health Plan chief executive James Roosevelt Jr. is a candidate to run the Social Security Administration, the program his grandfather signed into law in 1935, according to people briefed on the matter.

Roosevelt, 67, is the grandson of President Franklin Delano Roosevelt and would come to the commissioner’s post at time when the agency is facing intense financial and political pressures. He helped lead a review of the Social Security Administration as part of President Obama’s transition team, and previously served as associate commissioner for retirement policy for the agency under President Clinton.