The revised package now heads back to the House, where Republican leaders are hoping to approve it and send it to Trump before a self-imposed July 4 deadline. But it faces hurdles.

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.

Party leaders were able to muscle through considerable internal rifts, but the bill’s fate in the House was uncertain.