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.

Chris LaCivita, a top adviser to President Donald Trump, insists that Elon Musk will not cut Social Security in his pursuit to limit government because Musk is “not president” and therefore “doesn’t get to make those decisions.

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