WASHINGTON—Struggling Republican speaker nominee Rep. Jim Jordan postponed to Friday morning a third floor vote after a plan to temporarily put caretaker speaker Rep. Patrick McHenry in charge of the House ran into sharp objections from conservatives.

Jordan’s push to have a third vote on his candidacy Thursday fell apart as the Ohio conservative met continued resistance from his opponents during a meeting in a House office. As some trickled out, there was no sign he had managed to change their minds.