A prudent approach to reform would target the causes of the system’s shortfall with a mix of modest benefit cuts and modest tax increases. It would make sense, for instance, to trim the benefits of recipients who were high earners during their work lives, because, in general, high earners live longer than low earners and thus draw their relatively higher benefits for a longer period of time. Another sensible reform would be to bring more tax revenue into the system by raising the level of wages subject to Social Security taxes, currently $118,500. In recent decades, the wage cap has not kept pace with the income gains of high earners; if it had, it would be about $250,000 today.

The next move on Social Security is Mr. Trump’s. He can remind Republicans in Congress that his pledge would lead him to veto benefit cuts to Social Security if such legislation ever reached his desk. When he nominates the next commissioner of Social Security, he can choose a competent manager, rather than someone who has taken sides in political and ideological debates over the program.

What Mr. Trump actually will do is unknown, but his actions so far don’t inspire confidence. By law, the secretaries of labor, the Treasury and health and human services are trustees of Social Security. Mr. Trump’s nominees to head two of these departments, Labor and Treasury — Andrew Puzder, a fast-food executive, and Steve Mnuchin, a Wall Street trader and hedge fund manager turned Hollywood producer — have no government experience and no known expertise on Social Security.

His nominee to run the Department of Health and Human Services, Tom Price, a Republican congressman from Georgia, has been a champion of cuts to all three of the nation’s large social programs — Medicare, Medicaid and Social Security. When discussing reforms to Social Security, he has ignored ways to bring new revenue into the system while emphasizing possible benefit cuts through means-testing, private accounts and raising the retirement age.

There is no way to mesh those ideas with Mr. Trump’s pledge. But Mr. Price, who currently heads the House Budget Committee, has found a way to cut Social Security deeply without Congress and the president ever having to enact specific benefit cuts, like raising the retirement age. Recently, he put forth a proposal to reform the budget process by imposing automatic spending cuts on most federal programs if the national debt exceeds specified levels in a given year. If Congress passed Mr. Trump’s proposed tax cut, for example, the ensuing rise in debt would trigger automatic spending cuts that would slash Social Security by $1.7 trillion over 10 years, according to an analysis by the Center for American Progress, a liberal think tank. This works out to a cut of $168 a month on the average monthly benefit of $1,240. If other Trump priorities were enacted, including tax credits for private real estate development and increases in military spending, the program cuts would be even deeper.