Final answer:
The power that gives Congress the ability to pressure executive branch agencies is called the power of the purse.
Step-by-step explanation:
The power that gives Congress the ability to pressure executive branch agencies and secure compliance with congressional wishes is called the power of the purse. This power allows Congress to control funding and allocate money to agencies based on their compliance with congressional directives. Congress can reward compliant agencies by allocating more money to them, while cutting the budgets of non-compliant agencies.