WASHINGTON—The House of Representatives was headed toward a final vote Thursday to pass President Trump’s sprawling tax-and-spending bill, after Republican Party leaders worked through resistance from a handful of rank-and-file members.

The expected passage by the House means Congress would get the bill to Trump’s desk by his self-imposed July 4 deadline. The legislation funds Trump priorities including the extension of 2017 tax cuts, no tax on tips and overtime, and a funding boost for immigration and border policies.