WASHINGTON—For decades, conservatives have tried—and largely failed—to fundamentally reshape the federal government. If Donald Trump retakes the White House, they might succeed.

In campaign speeches and statements, the former president has promised to eliminate the independence of key federal agencies, reduce protections for civil servants, deny citizenship to tens of thousands of people born in the U.S. and wrest control of some authority over spending from Congress. If implemented, those measures and others Trump has proposed would amount to the most sweeping overhaul of the government in modern times, legal scholars said.