WASHINGTON—House GOP leaders are considering trying to pass a short-term spending bill that would keep the government funded into January, lawmakers and aides said Wednesday, potentially pushing debates over immigration and other contentious issues into next year.

The government’s current funding expires at 12:01 a.m. on Dec. 9, and lawmakers previously said they wanted to pass a two-week patch that would expire before Christmas. Lawmakers hoped that would give them enough time to write and approve a more detailed spending...