Washington (CNN) Donald Trump will be the next president, and Congress has to figure out what that means.

Democratic leaders woke up Wednesday facing two years in the wilderness and a big dilemma: Play to the liberal wing of their caucus and battle Trump tooth-and-nail -- or cater to the moderate Democratic faction eager to cut deals, even if it means some wins for the White House.

Republican began struggling to answer a basic question: Will Trump push more traditional GOP legislation or stick with the populist and polarizing proposals -- like his wall on the Mexican border -- he championed on the campaign trail?

No one quite knew the answer.

"I think we all agree this was a stunning election," Senate Majority Leader Mitch McConnell told reporters.

The incoming administration's approach could become clearer Thursday when Trump meets with House Speaker Paul Ryan, after a visit at the White House with President Barack Obama. Ryan on Thursday will also meet with Vice President-elect Mike Pence. The Indiana governor, a one-time member of the House Republican leadership, has a series of closed-door meetings on Capitol Hill Thursday. Pence will also meet with Vice President Joe Biden.

Ryan has moved quickly to lock down support within his conference to be reelected speaker, with no threats yet emerging to his leadership spot. McConnell planned to soon hold talks with Trump about plans for the first 100 days of the Republican's administration.

But it put immediate pressure on the likely two next Democratic leaders in Congress: New York Sen. Chuck Schumer and California Rep. Nancy Pelosi. While both are progressive Democrats and are expected to be elected as leaders of their respective caucuses, they may find it difficult to stay on the same page tactically given the different political imperatives of their caucuses.

For Schumer, the challenges will be formidable. He'll have to listen to the vocal and outspoken progressive wing of his caucus, led by Massachusetts Sen. Elizabeth Warren and Vermont Sen. Bernie Sanders, who have legions of supporters. But he also has five red-state Democrats in states Trump won convincingly -- Indiana, Missouri, Montana, North Dakota and West Virginia -- up for re-election in 2018. And if Schumer takes his caucus too far to the left, he's bound to could put his moderates in a difficult political spot.

Sen. Joe Manchin, a West Virginia Democrat who plans to run for reelection in 2018, warned his party not too move too far to the left.

"If the instinct of the party is to fight Donald Trump, then that's the stupidest thing that could happen," Manchin told CNN on Wednesday. "I will denounce my party and chastise them if they play that game."

Manchin added: "The bottom line is you can't govern from (the left) wing of the party. And if Chuck Schumer or the national Democratic Party ever wants to be a majority, they have to go to the middle."

For his part, Schumer is handling the Trump presidency carefully, noting that Trump called him Wednesday and that he'd look for areas over which they could agree.

"It's time for the country to come together and heal the bitter wounds from this campaign," Schumer said in a statement. "Senate Democrats will spend the coming days and weeks reflecting on these results."

Nancy Pelosi's future

Pelosi, representing a more liberal caucus, may be predisposed to battle the GOP agenda to the brink.

House Democrats, shell-shocked by Trump's win and much smaller than expected gains in their ranks, spent Wednesday mourning Clinton's loss and struggling to pinpoint what went wrong. They huddled on a conference call with Pelosi Wednesday afternoon.

Pelosi did not officially say she was running for re-election as the minority leader, but some Democrats on the call interpreted her posture -- laying out her thoughts on party's strategy moving forward -- as a sign she may want to stay and fight.

There is some concern among some House Democrats about Pelosi keeping the top spot because some in the caucus believe Tuesday's blowout in House races should trigger some kind of leadership shakeup. Those Democrats elected in the last couple of election cycles have mulled over whether the leadership table needs a younger face to represent the future of party. But no Democrat has signaled a challenge to her, and Pelosi's sharp political skills and relentless fundraising efforts are unmatched so it's unclear who would be able to cobble up enough support to force a change.

Pelosi took the pulse of members, but also gave a pep talk about what they could still accomplish in the minority with a new Republican in the White House, suggesting they could wield power and have a greater voice since in recent years their proposals were overshadowed by President Obama's bully pulpit.

The top House Democrat spoke by phone with Trump after she talked to her own members, and seized on one area where she saw an opening -- his proposal to add millions of federal dollars to build roads and bridges. Both Clinton and Trump emphasized proposals on the trail, but many House conservatives were alarmed at the price tag of the Republican plan's -- something Pelosi recognized as a way to drive a wedge in the GOP over the issue and complicate Ryan's job.

New York Democratic Rep. Joe Crowley, told CNN he also viewed infrastructure as an area where there could be bipartisan agreement on Capitol Hill.

But he also stressed that the party needed to make a better case for itself to reach out to those disaffected voters looking for change.

"We the Democrats have been the party of working men and women, Crowley told CNN, adding, that going forward "I think we have to retool that message so that people understand that we are standing up for them."

No threat to Ryan's job -- yet

Ryan moved to quickly put his splits with Trump in the rear view mirror, praising the President-elect at a press conference in Wisconsin, saying his win was "the most incredible political feat I have seen in my lifetime."

Some Republicans viewed Trump's victory speech in the early morning hours on Wednesday as an olive branch to Ryan and other Republicans, saying he wanted to work with those within his own party who disagreed with him.

"I think he has set the tone for a very collaborative process with Paul at the helm of the House and I think that is great," Rep. Kevin Cramer, R-North Dakota, a strong supporter of Trump's told CNN, suggesting that the businessman is already helping to smooth over any bad feelings those inside the party. He was optimistic that both Ryan and Trump could use each other's strengths to get a lot of key agenda items enacted quickly.

Ryan told House Republicans on a Wednesday conference call that he was running for another term. GOP sources on the call tell CNN that the speaker and other top leaders informed members leadership elections are moving ahead as planned next week.

Multiple House Republicans tell CNN that no one has signaled a challenge to Ryan or any of the top House GOP leaders. For now, the team appears to be moving quickly to avoid intraparty tensions by focusing rank and file members on their work with a new Trump Administration.

But a chunk of House conservatives who were completely unprepared for a Trump win admit that they expected to be hatching plans on how to deal with an expected Democratic takeover of the Senate. These members, many in the House Freedom Caucus, are still figuring out whether the Republican upset and strong hold on both chambers of Congress can be leveraged for more demands on Ryan to give them a greater voice in the House Republican conference.

Wednesday's call with members was in a "listen only" mode so members did not get the chance to press leaders on specific plans.

Ryan's spokeswoman AshLee Strong said Ryan "congratulated members who won re-election, and walked through the upcoming schedule. He used most of the time to discuss the huge potential ahead for House Republicans to work with president-elect Trump on behalf of the American people."

McConnell says he and Trump will hash out disagreements in private

McConnell held a wide-ranging news conference in the Capitol where he discussed the election, his priorities for the post-election lame duck session and the new Congress. As upbeat as he was about the results, he couldn't hide the reality that he has many differences with the surprise winner of the White House.

Asked three times by CNN if he supports Trump's signature plan to build a wall with Mexico, McConnell would only say, "I want to achieve border security the way that's most effective."

On the issue of term limits for lawmakers, something Trump has embraced, McConnell said no. "I would say we have term limits now, they're called elections. And it will not be on the agenda in the Senate," he said.

And McConnell pointedly disagreed with Trump's criticism of NATO. "I think the NATO alliance is every bit important today as it ever was. I think Article 5 means something. You attack any member of NATO you have us to deal with. I want the Russians to understand that fully," he said.

Despite that, McConnell says he expects to largely agree with Trump on the key issues and where he disagrees he will do so privately.

"I think most of the things that he's likely to advocate, we're going to be enthusiastically for," McConnell said. "Where we have differences of opinion, I expect to discuss them privately and not sort of hashing them out in public."

McConnell also said he would be careful not to misread the election as a mandate, something he said Democrats did in 2008 when Obama won the White House and with the help of a Democratic-controlled House and Senate pushed through Obamacare, banking reforms, and the economic stimulus package over the objections of Republicans.

"We've been given a temporary lease on power, if you will," McConnell said. "And I think we need to use it responsibly."