WASHINGTON (AP) — Republican leader Kevin McCarthy won the nomination Tuesday for House speaker, clearing a first step with majority support from his colleagues, but he now faces a weeks-long slog to quell right-flank objections before a final vote in the new year.

McCarthy has led House Republicans this far, and with the party now on the cusp of majority control, he has a chance to seize the gavel from Nancy Pelosi if Democrats are defeated.

The GOP leader pushed through the internal party election on a 188-31 vote, with ballots cast by new and returning lawmakers, but the challenges ahead ar...