The involvement of Antonio Gracias, an investor who has known Elon Musk for two decades, suggests that Mr. Musk has made overhauling the Social Security Administration a priority.

Pinned to the top of Elon Musk’s X account is a six-minute clip of his recent three-hour interview with the podcaster Joe Rogan.

Although federal officials have long recognized improper spending as a problem, it is not the main reason for the program’s dire financial outlook