Republican presidential candidate Ted Cruz’s tax plan would cut projected federal revenue by about a fifth over the next decade, according to a new analysis—a hit that would require sizable spending cuts to meet his goal of balancing the federal budget.

Mr. Cruz’s plan would reduce federal tax collections by $8.6 trillion over 10 years, and that doesn’t include additional interest on extra debt, according to the Tax Policy Center’s analysis, released Tuesday. High-income households would be the biggest beneficiaries of a...