House Democratic Leader Steny Hoyer told reporters Wednesday morning that he's concerned about the slim Democratic majority heading into the next session of Congress, given Biden's decision to pluck certain members for his administration.

Rep. Cedric Richmond was tapped as a senior White House adviser and Rep. Marcia Fudge as secretary of Housing and Urban Development, according to sources.

Hoyer said he told Biden's team to be "very careful" in terms of who it selects to join the team. Democrats are breathing easier knowing that Richmond and Fudge's respective seats are relatively safe Democratic seats -- but special elections take time, so the margins in the House will be incredibly tight in the coming weeks and months ahead.

"I’m certainly concerned by the slimming of the majority. I indicated to the administration very early on that I wanted them to be very careful in terms of the members that they appointed from Congress given the closeness of our majority," Hoyer said.

"I think, frankly, we're going to be a very unified caucus, as we were this past Congress," Hoyer added. "The American people are confronting two great crises: one a health crisis and the other an economic crisis, and they expect us to come together as a Congress on their behalf."

-ABC News' Mariam Khan

Intra-party rumblings about diversity and experience are more than background noise as Biden builds out his governing team. The relatively drama-free transition has masked concerns about whether Biden's decisions can meet his commitments -- with implications for governance after Jan. 20.

Biden's choice of California Attorney General Xavier Becerra to lead Health and Human Services puts a Latino in a high-profile spot, though Biden's stumble over his last name wasn't the best introduction to the country.

Rep. Marcia Fudge at Housing and Urban Development  in the Cabinet, and Biden's choice of retired Gen. Lloyd Austin -- who will be introduced by Biden and Vice-president-elect Kamala Harris Wednesday -- would put a Black man in charge of the Pentagon for the first time ever.

Still, coming out of Biden's meeting with prominent Black leaders Tuesday night, some want Biden to create a new high-ranking advisory job -- and Black and Latino activists and advisers are focused on the attorney general's job as well.

The choice of Austin is also leaving Democrats worried about preserving civilian control over the Defense Department. For some, that will mean explaining why a Trump appointment of a recently retired general shouldn't have gotten a legal waiver to serve in the role, while a Biden one should.

Just last week, Biden re-set his high bar: "I promise you, it'll be the single most diverse Cabinet based on race, color, based on gender, that's ever existed in the United States of America," he told reporters.

He is making picks that move him in that direction. But the unity Democrats have found in opposing the Trump White House is showing signs of strain as names roll out -- to say nothing of policy.

-ABC News' Political Director Rick Klein

Trump has vowed to intervene in a long-shot lawsuit filed by the state of Texas directly to the Supreme Court  Tuesday seeking to toss out ballots in four states where Biden won as he continues his campaign to overturn the results of the presidential election.

“We will be INTERVENING in the Texas (plus many other states) case. This is the big one. Our Country needs a victory!” Trump tweeted Wednesday morning.

The state of Texas filed a lawsuit Tuesday against Michigan, Wisconsin, Pennsylvania and Georgia, arguing that those states “exploited the COVID-19 pandemic to justify ignoring federal and state election laws and unlawfully enacting last-minute changes, thus skewing the results of the 2020 General Election.”

Justices have not said whether they'll weigh the case, but legal experts say it's is unlikely to succeed.

Trump provided no details on how he would intervene.

The tweet comes after the Supreme Court on Tuesday denied a request from Trump allies to stop the certification of Pennsylvania's election results -- a case Trump said had "nothing to do with him" on Wednesday.

Notably, before the Supreme Court's denial came in, Trump called on the justices to have the "courage" to intervene at an event on coronavirus vaccines at the White House.

"Now, let's see whether or not somebody has the courage -- whether it’s a legislator or legislatures, or whether it's a justice of the Supreme Court or a number of justices of the Supreme Court. Let's see if they have the courage to do what everybody in this country knows is right," he said Tuesday.

-ABC News' Devin Dwyer

Biden is slated to introduce his nominee to lead the Defense Department, retired four-star Gen. Lloyd Austin, from Wilmington, Delaware, on Wednesday.  But the nomination of the first African American to the helm the Pentagon is facing some resistance.

Because defense secretaries are legally required to have been retired from active duty for at least seven years to ensure civilian control of the U.S. military, and Austin retired in 2016, he would require a waiver to hold the position. Congress approved the waiver for retired Gen. James Mattis, Trump’s first defense secretary, but some Democrats, including Sens. Elizabeth Warren and Richard Blumenthal, have expressed a desire to return to normal protocols in a Biden administration despite the historic nature of Austin's nomination.

Biden is also expected to name former Iowa Gov. Tom Vilsack as secretary of Agriculture and Rep. Marcia Fudge, D-Ohio, as secretary of Housing and Urban Development as he continues to build out his Cabinet -- one he says will be the most diverse in American history.

Fudge’s appointment, however, would shave another slice away from House Democrats’ already razor-thin majority -- giving them just two extra votes on top of the 218 needed to pass a bill through the chamber. Special elections are expected to bump Democrats back up to 222 seats, but those take time. And if Congress can’t pass more relief aid in the lame duck session, the Biden administration will want a solid House majority to pass a package from the onset.

As the president-elect rolled out his health team Tuesday, he also spelled out specific steps toward getting the coronavirus under control in his first 100 days in the White House, including a mask campaign and executive order requiring one be worn on federal properties, at least 100 million vaccinations “into the arms of the American people" and making reopening schools a “national priority.”

While Biden is pushing forward, Trump isn’t backing down. He continued to falsely claim he won the election in key swing states where Biden actually was victorious at a self-congratulatory vaccine “summit” Tuesday.

With the passing of the “safe harbor” deadline when Congress considers states' results conclusive and the Supreme Court’s denial of an 11th-hour attempt by Trump’s allies to block certification of the election results in Pennsylvania, time is running out for the Trump’s long-shot legal challenges with the Electoral College meeting in less than a week. The Supreme Court could still weigh in on a Texas filing against Georgia, Michigan, Pennsylvania and Wisconsin to turn the election for Trump, but experts say it’s unlikely to gain traction.