WASHINGTON—House Speaker Mike Johnson (R., La.) unveiled a two-step short-term spending proposal that would keep money flowing to federal agencies into early next year, in a bid to stave off a partial government shutdown later this week. 

Johnson presented the plan on Saturday, a week before federal agencies risk shutting down once current funding runs out. The measure wouldn’t impose spending cuts, and it also wouldn’t implement tougher anti-immigration rules at the U.S.-Mexico border, which some Republicans had said was critical to get their support.