WASHINGTON—President Biden heads into the end of the year with deepening Democratic worries about his re-election, as his effort to aid allies in two wars hangs in the balance on Capitol Hill and an impeachment inquiry into him and his family moves forward. 

At the same time, some rays of hope are peeking through for the incumbent as a tough 2024 contest looms, with the Dow Jones Industrial Average reaching a record high and—perhaps most important from an electoral perspective—consumer confidence rebounding this month faster than expected.