Members of Congress are still unpacking the results of the midterm elections, but they will return Monday to Washington with plenty to do, from funding the government to authorizing key defense programs.

Senate Majority Leader Charles E. Schumer over the weekend said senators should expect “heavy work” and “long hours” even as the final makeup of next year’s Senate hinges on a December run-off election in Georgia and key House races remain unsettled.

Most notably, Congress must pass a funding bill before Dec. 16 to avoid a government shutdown. Democrats could try to add special provisions to the bill — including funding for Ukraine’s war effort and the COVID-19 fight — because the GOP is poised to take over the House and is more skeptical of those efforts.

A second priority is the National Defense Authorization Act, or NDAA, a bill that outlines defense priorities and authorizes funding for them. Increased funding for Taiwan’s security in the face of Chinese threats and possible moves to punish Saudi Arabia for its decision to cut oil production may be considered.

On the Senate side, Mr. Schumer has promised to hold a vote on a bill that would codify the right to same-sex marriage instead of relying on the 2015 Supreme Court decision that made it legal across the U.S.