Helping erase employees’ student loan debt is a no-brainer to some companies. The big question is whether to tackle the problem solo or wait for Congress to chip in with new tax breaks.

Willis Towers Watson predicts that one-third of employers will pitch in on paying back loans by 2021. Roughly 4 percent of companies offer debt repayment options today, the global advisory firm says.

Devising ways to wipe out the tens of thousands in student loans modern workers shoulder...