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.

This time, Senate Republicans were dead-set on making an expensive suite of pro-growth business tax cuts permanent. That required finding deep offsetting cuts, and the cold, hard calculus by the Senate GOP’s chief architects was that enough of their 53-member conference would ultimately swallow their protests and go along.