Final answer:
The War Powers Act limits the president's ability to send troops without a declaration of war by requiring notification to Congress within 48 hours of deployment and barring forces from remaining in conflict beyond 60 days without Congressional approval.
Step-by-step explanation:
The law that limits the president's ability to send troops without a declaration of war is the War Powers Act. Passed in 1973 over President Nixon's veto, the War Powers Act requires the president to notify Congress within forty-eight hours of deploying troops and restricts the use of armed forces in hostilities to a sixty-day period without Congressional authorization or a declaration of war, extendable by thirty days if needed for withdrawal.
Although intended to check the president’s power, the Act in practice permits the president to initiate military action for up to ninety days, including the option for a thirty-day withdrawal, which some argue enhances the president's unilateral war-making authority in the short term.
Through various means such as UN resolutions and congressional authorizations, presidents have engaged in military actions since World War II without official declarations of war. The War Powers Act was meant to rein in this power post-Vietnam War, amid concerns over the executive branch’s growing war-making capabilities.