Joe Biden promised he would push to cancel a significant portion of Americans’ student debt during his presidential campaign. Fulfilling this promise entails politically fraught decisions over how to do it and who would benefit.

Mr. Biden, a Democrat, campaigned on forgiving hundreds of billions of dollars of student debt, starting with a $10,000 write-off for all 43 million Americans with federal loans. Some congressional Democrats and activist groups are pushing him to go further, forgiving most or all of the $1.6 trillion in student debt.

Student debt is the largest type of debt held by Americans after mortgages. The amount has tripled since 2007. Defaults are high. Many economists say that canceling at least some debt would boost the U.S. economy by reducing borrowers’ bills, leaving them with more money to spend on homes and cars, or even starting businesses.