WASHINGTON—Republicans squeaked President Trump’s tax-and-spending megabill through the Senate on Tuesday, capping a long night of dealmaking to win over holdouts and ending with a tiebreaking vote from Vice President JD Vance.

The Senate’s 51-50 action puts Republicans on the verge of locking in Trump’s top legislative priorities: extended tax cuts, new tax breaks, reductions in Medicaid spending and more money for defense and border enforcement. They are using their full but narrow control of Congress to pull money from safety-net programs and the clean-energy industry and redirect it to national security and taxpayers’ wallets.