The 2 percentage point increase is the result of the expiration of the payroll tax holiday, is expected to have a bigger impact on Family Dollar and other discounters' core customers. They're more likely to be living paycheck-to-paycheck.
Analysts have said this will hurt discount retailers. Levine said on CNBC's "Squawk on the Street" morning program that he doesn't think the tax will be a significant drag on his company.
"We've been through many economic scenarios that were much more challenging than this one," he said, although he added the payroll tax is "certainly not a positive."
Family Dollar's core customer is typically a person whose household income is $40,000 or less per year. The company saw more "trade-down" customers during the recession, when customers with incomes between $40,000 and $70,000 switched some of their shopping to Family Dollar as they sought to save money.
Levine said the trade-down customers are still seeking out Family Dollar, although he declined to break out what percentage of the retailer's customers they are. Levine said the core customers, with under $40,000 in annual income, remain the majority of Family Dollar's customers.
Family Dollar's latest earnings, reported earlier this month, disappointed investors and left the stock slumping as gross margin fell and the retailer lowered its forecast.