Doug Jones wins the Alabama Senate race -- what happens now?

Democrat Doug Jones has won the Senate race in Alabama. But what happens now, after this special election for now-Attorney General Jeff Sessions' seat? 

As far as opponent Roy Moore is concerned, it's not over yet. He did not concede Tuesday night. As of this writing, the margin is just over 1 percentage point for Jones, and that's larger than the automatic recount rule margin in Alabama of 0.5 percent. Moore seemed to be placing his hope for making up the difference in the military absentee votes, but CBS News' Anthony Salvanto believes that most of the absentee votes cast have already been included in these counts. Jones' lead is currently just over 20,000 votes, out of the 1.3 million cast.

If the margin remains greater than 0.5 percent and there is no recount, once Jones takes his seat, Republicans will still control the chamber, albeit by a narrow 51-to-49 seat margin. But tje timing on when he'll actually become a U.S. senator is still a little uncertain. 

Senate Majority Leader Mitch McConnell has said he expects Republican Alabama Sen. Luther Strange -- who was named to fill the seat right after Sessions was confirmed as attorney general -- to be here until the end of this session, which would be whenever they adjourn for Christmas recess. 

Otherwise Strange would be around until January 2 if they don't adjourn. The second session of the 115th congress starts on January 3.

The Alabama Board of Elections and Alabama secretary of state have said they have until December 22 for precincts to report the results to the canvassing board. State officials also said they don't expect the winner to come to D/C. before January 3.  

Jones is likely to arrive in Washington, D.C., when the new session begins on January 3. Before that date, Republicans hope to vote to vote on spending measures and their tax overhaul plan.

Meanwhile, Republican senators are planning to huddle together Wednesday morning to discuss their next moves. Sen. John Cornyn, the number-two Republican in the Senate, told CBS News on Tuesday that the GOP's tax overhaul efforts and the Alabama Senate race were likely to be discussed. 

CBS News John Nolen and Anthony Salvanto contributed to this story.