Final answer:
The correct term for the president letting a bill die without signature when Congress adjourns within ten days is a "Pocket Veto". It's a legislative power that cannot be overridden by Congress since they are out of session, demonstrating a check on congressional power by the Executive Branch.
Step-by-step explanation:
If Congress adjourns within ten days after submitting a bill, and the president chooses not to sign it, this is known as a "Pocket Veto". This legislative power allows the president to effectively veto the bill without having to return it to Congress with a veto message. In this scenario, because Congress is not in session to reconsider the bill or attempt to override the veto, the bill simply dies.
The presidential veto process serves as a significant check on congressional legislative powers. While a president can issue a regular veto with a message that sets out objections, it is possible for Congress to override such a veto with a two-thirds majority in both houses. However, the pocket veto cannot be overridden since by definition, Congress is not in session to respond.
The use of the pocket veto is a strategic tool for the Executive Branch, providing the President with the power to block legislation at the end of a congressional session without the risk of a congressional override. This exemplifies the system of checks and balances central to U.S. government operation.