What is the term used when the President refuses to sign a bill into law?

The term for when the President refuses to sign a bill into law is "veto." This action is a constitutional power that allows the President to reject legislation proposed by Congress. When a veto is exercised, the bill does not become law unless Congress can subsequently override the veto with a two-thirds majority in both the House of Representatives and the Senate.

Understanding this term is crucial because it highlights the system of checks and balances inherent in the U.S. government. The veto power enables the President to influence legislation and ensures that not all bills passed by Congress automatically become law, which allows the executive branch to have a significant role in the legislative process.