But first, the old Congress and the old president must wrap up year-end business in a so-called "lame duck session." The most important item is to avoid a government shutdown next month by negotiating a bill to fund federal agencies into next year when Donald Trump will be in the White House. Republicans and Democrats don't have a deal yet, but with the election results that had Republicans retain control of both chambers of Congress and win the White House, the GOP may feel they have leverage over wounded Democrats.
Current funding runs out December 9. Leaders would like to pass a deal by then -- if not they would have to approve a short-term bill of a week or two to keep the government operating while they negotiate.
"We have three more weeks to finish up this year's work," Senate Majority Leader Mitch McConnell said Friday, complaining that Democrats had blocked spending bills to this point over a variety of issues. "So we now have to figure out how to do that."
McConnell and House Speaker Paul Ryan haven't said exactly how they would like to pass the remaining spending bills. One option would be to tie the bills together and pass them as one giant "omnibus" spending package or as a series of smaller bills. That would keep the government running through October 1, 2017, and would ensure that the carefully tailored spending measures for each of the government agencies is in place.
But many conservatives hate the idea of passing one giant bill out of fear it's so big they can't reasonably know what's inside it. They prefer a shorter term "continuing resolution" that would fund the government at current levels into the spring so the Trump administration can put its stamp on government spending and reforms.
Over the next few weeks, lawmakers will be looking ahead too, readying for Trump to take the reins of power. Already members are discussing with Trump and his top aides how and when to repeal and replace Obamacare, what federal regulations should be cast aside when Trump is sworn-in, and how Trump can meet his campaign promises on immigration, border security, tax reform and other issues.
The session was expected to be far more consequential if Hillary Clinton was elected, but with the Republican set to take office in January, its already certain that two top priorities for President Barack Obama will die on the vine. His nomination of Merrick Garland to the Supreme Court that Republicans refused to act on in an election year will expire at the end of the year. Trump has said he'll name a much more conservative justice instead. And the long-sought trade deal, the Trans Pacific Partnership, which Obama negotiated but that Trump campaigned against, is also dead for the year.
Paul Ryan facing easier-than-expected vote
Before digging into talks over the government funding bill, the first order of business for both parties will be to hold leadership elections to prep for the next Congress.
Ryan, who didn't want the job just a year ago when former Speaker John Boehner stepped down, has clashed with both House conservatives and President-elect Trump in the last year.
Key members of the conservative House Freedom Caucus declined to commit to backing him for another term in the lead up to the election. But after Trump's upset victory Ryan quickly pivoted to mend fences with the President-elect. Ryan praised him for his ability to tap into the mood of the American electorate, and hosted Trump and his former House colleague, Vice President-elect Mike Pence in his Capitol office and began planning their agenda. Trump also seemed to smooth things over by turning the page on their past squabbles, and focusing on items they could quickly do together.
Ryan appears on track to gain another term as speaker when House Republicans huddle for a secret ballot vote on Tuesday afternoon.
And when it comes to getting business done next year, Sunday's naming of a fellow Wisconsin Republican, Reince Priebus, as Trump's incoming chief-of-staff should also help Ryan.
For congressional Democrats, Clinton's loss still stings. They also picked up far fewer House and Senate seats than expected on Tuesday night and face a new president who wants to undo virtually everything they put in place in the last eight years.
House Democrats initially planned to vote on their leadership posts at the end of November, but House Minority Leader Nancy Pelosi announced on Friday that the election is now scheduled for this Thursday.
Even though grassroots Democratic groups around the country are calling for a shakeup, Pelosi and the bulk of her leadership team appear poised to remain in place.
Chuck Schumer to succeed Harry Reid?
In the Senate, the leadership elections are planned for Wednesday. McConnell, Senate Republican Whip John Cornyn of Texas and most of their top team are expected to stay in place.
On the Democratic side, New York Sen. Chuck Schumer is expected to be elected leader. He replaces the tough-talking and hard-nosed Sen. Harry Reid of Nevada who has clashed with McConnell for years.
McConnell has been complimentary of Schumer in recent days, indicating he thinks the two will be able to cut deals, something McConnell struggled to do with Reid.
"Schumer and I have talked. He's a smart, transactional person. I think we'll get along fine," he said.
There is the potential for some drama in the Democratic leadership elections if Sen. Patty Murray of Washington, already a member of leadership, decides to challenge Sen. Dick Durbin of Illinois for his No. 2 post. Such a move could set off a bitter battle between the two and make for difficult decisions for their colleagues who would have to choose between the long-serving friends.
Murray has not said what she will do but CNN reported last week she was making calls to other Democratic senators to gauge support for a possible challenge.
Freshman orientation, Iran and Biden's cancer 'moonshot'
Almost 60 new members of the House and Senate will attend freshman orientation sessions this week when they will learn tips about hiring staff, running a congressional office, and abiding by strict ethics rules.
Notable freshman in the House include Charlie Crist, who was once a Republican governor of Florida, but will who arrive in Congress as a newly-elected Democrat representative from St. Petersburg. Also Lynn Cheney, the daughter of former Vice President Dick Cheney, takes the seat he once represented from Wyoming.
In the Senate, the arrival of Kamala Harris, D-California, means there will be three African-American senators serving in the Senate at the same time for the first time in history. She joins Sen. Tim Scott, R-South Carolina, and Sen. Cory Booker, D-New Jersey.
Congress is also expected to renew sanctions on Iran that are due to expire at the end of the year.
The only major piece of legislation expected to pass during the post-election "lame duck" session is an important bill to boost funding for modern medicine. The 21st Century Cures bill is backed by Republican on the Hill and the White House and is expected to become law.
The bill includes funding for Vice President Joe Biden's cancer "moonshot" he has spearheaded in the wake of the recent death of his son to brain cancer.