GEOFF BENNETT: Welcome to the "News Hour."

President-elect Donald Trump took a victory lap in the nation's capital today, bouncing from meetings with House Republicans to the Oval Office, which is soon to be his again.

AMNA NAWAZ: President Biden hosted Trump for nearly two hours, a familiar ritual in the peaceful handoff of power.

That comes as critical roles are being filled from more members of Trump's Cabinet to new leaders in the Senate.

Lisa Desjardins begins our coverage.

REP. MIKE JOHNSON (R-LA): The 47th president of the United States, Donald J. Trump.

LISA DESJARDINS: Donald Trump's big return to Washington echoed his rallies on the campaign trail, walk-up song and all.

DONALD TRUMP, Former President of the United States (R) and Current U.S. President-Elect: It's nice to win.

LISA DESJARDINS: The president-elect spoke to House Republican leadership for the first time since his victory last week, declaring GOP control of the Lower Chamber.

That is within reach, but it has not been called yet, with more than a dozen House races still uncertain.

DONALD TRUMP: We worked with a lot of you to get you in, and you helped me, and you helped me too.

LISA DESJARDINS: Much of the meeting happened behind closed doors.

REP. TOM COLE (R-OK): It was mostly kind of a replay of Donald Trump's greatest hits.

I think it was more just a reminder to the troops to hang together, get things done.

He intends to move pretty fast and strap it up and get ready.

LISA DESJARDINS: In the room was Elon Musk, reportedly greeted with a standing ovation one day after Trump named him, along with Vivek Ramaswamy, to lead a brand-new Department of Government Efficiency.

Despite its name, it is not a government entity or agency.

Those in attendance welcomed Musk to the party.

REP. NICHOLAS LALOTA (R-NY): Members acknowledge his presence and want him to be part of an administration moving forward that helps make our government more efficient.

REP. AUSTIN SCOTT (R-GA): We need these people that can bring in a new perspective, if you will, to how we run the agencies, and I think we can get more done with less money.

And so eliminating the deficit is obviously something that all Americans are concerned about.

JOE BIDEN, President of the United States: Donald, congratulations.

DONALD TRUMP: Thank you.

LISA DESJARDINS: From there, Trump returned to the White House itself with a handshake and a nod to the coming handoff from President Joe Biden.

JOE BIDEN: Looking forward to having a, like we said, smooth transition.

Do everything we can to make sure you're accommodated, what you need.

And we're going to get a chance to talk about some of that today.

LISA DESJARDINS: Meetings between incoming and outgoing presidents are traditional, but, in 2020, then-President Trump did not extend an invite to then president-elect Biden.

In the Oval Office today, they both pledged a smooth transition.

DONALD TRUMP: Politics is tough, and it's, in many cases, not a very nice world, but it is a nice world today.

And I appreciate it very much, a transition that's so smooth.

It'll be as smooth as it can get.

And I very much appreciate that, Joe.

JOE BIDEN: You're welcome.

LISA DESJARDINS: Notably absent from today's visit, the incoming first lady, Melania Trump.

The White House says Jill Biden wrote her a letter and is prepared to assist her with the transition.

Trump announced four names today to his new White House, all of them close campaign advisers, Stephen Miller as deputy chief of staff for policy and homeland security adviser, as well as Dan Scavino, James Blair, and Taylor Budowich.

They will all serve as deputy chiefs of staff.

Trump has tapped former representative and former Democrat Tulsi Gabbard to serve as director of national intelligence and a bombshell choice for attorney general, Florida Representative Matt Gaetz, a staunch Trump loyalist who has been an elected politician for most of his adult life.

He would step into the role of the nation's top prosecutor.

Meantime, on Capitol Hill, after two rounds of voting, Senate Republicans emerged with their first new leader in nearly 18 years, choosing John Thune, the senior senator from South Dakota, known outside the Senate as a communicator and inside it for good relationships with all corners of the party.

SEN. JOHN THUNE (R-SD): The American people have loudly rejected the failed policies of the Biden/Harris/Schumer agenda.

And this Republican team is united.

We are on one team.

We are excited to reclaim the majority and to get to work with our colleagues in the House to enact President Trump's agenda.

LISA DESJARDINS: But to win, 63-year-old Thune had to address his past breaks with Donald Trump.

In 2016, after the release of the "Access Hollywood" tape, in which Trump bragged of assaulting women, Thune called on Trump to leave the presidential race.

Then, in 2020, Thune decried Trump's efforts to overturn the election results in Congress.

Trump fired back that Thune was a RINO, Republican in name only, threatening that his political career was over.

Thune worked this year to repair the relationship, meeting with Trump in March, and recently writing that he is open to Trump's demand for potential recess appointments.

He spoke to that today.

SEN. JOHN THUNE: Well, what we're going to do is make sure that we are processing his nominees in a way that gets them into those positions so they can implement his agenda.

I have said this, and I mean it, that we expect a level of cooperation from the Democrats to work with us to get these folks installed.

And, obviously, we're going to look at, explore all options to make sure that they get moving, that they get moved quickly.

LISA DESJARDINS: Leader Thune's relationship with Trump will be a test for both men and for the Senate itself, which has traditionally stood as a check on executive power, whether the president is a member of your party or the opposite party -- Geoff.

GEOFF BENNETT: And, Lisa, what does Senator Thune's election, his elevation as Republican leader now, what does that tell us about the GOP-led Senate?

LISA DESJARDINS: That's right.

It tells you that this is a place that still values institutions and traditions, as well as the way the Senate has functioned for most of modern politics.

And the reason here is, this was a furious push from MAGA Trump-aligned Republicans to try and get in who the person they saw as the most loyal Trump supporter, someone who wanted to change the way the Senate operated.

Instead, the senators in secret ballot measures voted for John Thune.

And part of that too is the way senators themselves work.

They clearly are saying that they believe John Thune is the one who can help them and help the Senate get things done the best.

GEOFF BENNETT: Lisa, I know you're also tracking control of the House.

Bring us up to speed.

What's the latest?

LISA DESJARDINS: All right.

Let's take a look, guys.

We are getting very close to Republicans clenching control of the House right now.

According to Associated Press calls, 207 seats Democrats have won, 217 seats Republicans have won.

And I want to take a look at the map in particular, at the seats that are still remaining.

You can see some of these.

If you look over at Alaska there, you can see it's a shade of pink that the Republicans are leading there.

However, Democrats are leading somewhere else, in Oregon.

Now, you do all this math together.

We have all been doing it for the last couple of days.

And in the end, we're seeing things break about even at this point.

The House Republicans are on track at this moment to pick up a single seat, not a lot, in the House.

GEOFF BENNETT: But, Lisa, Donald Trump, the president-elect, he continues to nominate members of the House to serve in his administration, Elise Stefanik, Matt Gaetz.

What does that do to the numbers?

LISA DESJARDINS: That's a real problem for House Speaker Mike Johnson and his team.

They already were struggling with close margins before, but let's kind of break down what happens here.

Right now, the House, as I said, is on track to pick up one seat, so that would be 222 Republicans.

Now, if three members go to the Trump administration, if it's not more than that, then that would leave Republicans with 219, at least temporarily, Republicans.

And what does that mean?

They can only lose three votes on anything.

This gives more power to different factions within the Republican Party.

And I can report right now talks are under way about that motion-to-vacate rule, whether that should be extended and increased.

That would give Speaker Johnson more protection, but there's no agreement on that yet.

One other note, the House did vote, the House Republicans did vote to install the replacement for Elise Stefanik.

Her name is Lisa McClain, representative of Michigan.

She will be the new conference leader, the messenger of House Republicans' message in politics going forward.

GEOFF BENNETT: Lisa Desjardins on this busy day on Capitol Hill.

Lisa, thanks, as always.

LISA DESJARDINS: You're welcome.