The counting continues in Georgia, where Republican Senator David Perdue is trying to hold off Democrat Jon Ossoff in a multi-candidate race that could also go to a runoff if neither candidate clears the 50 per cent threshold to win.
There is already a January 5 runoff in the state's other Senate race. Republican Senator Kelly Loeffler will face Democrat Raphael Warnock, a black pastor at the church where Martin Luther King Jr preached, after they emerged as top vote-getters, but failed to clear the majority threshold.
Democrats face long but not fully impossible odds to take a slim majority after a disappointing election night where Republicans defeated multiple challengers.
McConnell, who secured a seventh term for himself in a costly campaign against Democrat Amy McGrath, a former fighter pilot, has said he felt "pretty good" about the remaining contests.
But Democrats remain hopeful. Strategist Zac Petkanas said the 2020 election "was going to be an awful, ugly, dirty slog until the bitter end".
Securing a Senate majority will be vital for the winner of the presidency. Senators confirm administration nominees, including the Cabinet, and can propel or stall the White House agenda. With Republicans now controlling the chamber, 53-47, three or four seats will determine party control, depending on who wins the presidency.