As Democrats face the reality of President Trump’s second term, they share a fundamental belief: This moment calls for an inspirational message from their party.

They just cannot decide what, exactly, that should be.

In private meetings and at public events, elected Democrats appear leaderless, rudderless and divided. They disagree over how often and how stridently to oppose Mr. Trump. They have no shared understanding of why they lost the election, never mind how they can win in the future.

And in a first step toward elevating new leaders, an election this weekend for chair of the Democratic National Committee, the party chose a candidate, Ken Martin of Minnesota, who said he planned to conduct a post-election review largely focused on tactics and messaging. Mr. Martin said he had not determined the parameters of the review, other than that he was not interested in discussing whether former President Joseph R. Biden Jr. should have sought re-election.

More than 50 interviews with Democratic leaders revealed a party that is struggling to define what it stands for, what issues to prioritize and how to confront a Trump administration that is carrying out a right-wing agenda with head-spinning speed. Governors, members of the Senate and the House, state attorneys general, grass-roots leaders and D.N.C. members offered a wide range of views about the direction of their party.

Their concerns are spilling out into public, as the country’s most powerful and prominent Democratic politicians air sharp disagreements over how aggressively they should oppose Mr. Trump.

“We’re not going to go after every single issue,” Senator Chuck Schumer of New York, the minority leader, said in an interview. “We are picking the most important fights and lying down on the train tracks on those fights.”

Plenty of Democrats think that picking battles is the wrong approach when dealing with a president who is willing to disregard constitutional norms and legal guidelines.

On a private call with Mr. Schumer last week, a half-dozen Democratic governors pressed him to be more aggressive in opposing the entire Trump agenda — not just those issues on which the party thinks it can score strategic victories.

“He is not somebody that you can appease,” Gov. JB Pritzker, an Illinois Democrat, said in an interview. “We’ve got to stand up and fight. And by the way, at the state level, I think many of us are. But I think that we’ve got to make sure that in the Senate and the House, that the people who have a platform are standing up.”

Democrats broadly agree that they need to do more to address the issues that powered Mr. Trump’s campaign, like grocery costs, inflation and immigration. But there is little consensus on how — or even whether — to prioritize the party’s traditional concerns like abortion rights, L.G.B.T.Q. equality and climate change. Some Democrats fear that even as those issues continued to animate the party’s base, they failed to resonate among a broader swath of voters in the last presidential election.

“We have no coherent message,” said Representative Jasmine Crockett, Democrat of Texas. “This guy is psychotic, and there’s so much, but everything that underlines it is white supremacy and hate. There needs to be a message that is clear on at least the underlying thing that comes with all of this.”

Still, a healthy segment of the party believes that a narrow focus on the economy is the best way to win back voters who supported Mr. Trump because they hoped he would lower prices and make their lives easier.

“There are people in the middle — and trust me, there’s a lot of them — that wanted costs to go down,” said Senator Amy Klobuchar, Democrat of Minnesota. “Instead, what they see is chaos going up, corruption going up with the firing of the inspector generals, and guess what else is going up? Egg prices.”

The fortunes of the party may depend on how Mr. Trump’s disruptive policies are received. His announcement on Saturday that he would impose stiff tariffs on Mexico, Canada and China added a new layer of economic uncertainty that could provide an opening for Democrats.

The tepid race for D.N.C. chair illustrated the lack of a broad party message that goes beyond attacking Mr. Trump to offer a new vision.

As party members gathered in Washington this weekend, they heard from candidates for chair who offered largely tactical solutions and fiery attacks on Mr. Trump that echoed the party’s message eight years ago. The eventual winner, Mr. Martin, offered a diagnosis that was all about how the party communicated, rather than what it was saying.

“The policies that we support and the message that we have is not wrong,” Mr. Martin said in an interview after his victory. “It is a messaging problem and a brand problem. Those voters are not connecting our policies with their lives.”

Mr. Martin acknowledged that he would have to smooth over some internal divisions in the party. He won despite being opposed by some of the party’s most significant elected officials and donors. His top rival, Ben Wikler, the Wisconsin Democratic chairman, was backed by Mr. Schumer; Representative Hakeem Jeffries of New York, the House Democratic leader; Representative Nancy Pelosi of California, the former House speaker; a stable of Democratic governors; and the liberal billionaire donors Reid Hoffman and Alexander Soros.

Representative Josh Gottheimer, a Democrat who is running for governor of New Jersey, said the party must reset its message to focus more intensely on affordability — lowering costs of housing, groceries and child care.

“Within the party, we need to make sure we have a very clear direction to go,” he said. “We need to have our own ideas. We’ll never win again if we are just playing defense.”

Many Democrats believe any evolution will come not from leaders in Washington but from what many see as a strong bench of governors, attorneys general and state legislators. Mr. Martin acknowledged that the party’s 2028 presidential primary race — probably two years away from fully beginning — would go a long way toward determining an affirmative Democratic message. Mr. Martin sees his job largely as reshaping the party’s infrastructure — including Democratic ad spending, data collection and state party resources — for a future in which the Sun Belt becomes more politically dominant than the Rust Belt.

In private discussions, former President Barack Obama has compared this moment to early 2005, after Democrats had lost the White House and control of Congress, according to a person briefed on the conversations. Two years later, Democrats gained control of Congress. And two years after that, Mr. Obama became the country’s first Black president and re-energized the party.

“We’re going to have midterm elections quicker than you may know,” said former Gov. Jay Inslee of Washington State. “And the last time we picked up all kinds of seats, and I’m looking forward to that again.”

Yet there is little question that for now, at least, Democrats are at a low point.

A Quinnipiac University poll conducted the week after Mr. Trump took office found that 57 percent of voters viewed the Democratic Party unfavorably — the highest level since 2008.

Eight years ago, after Mr. Trump’s first victory, party officials followed the lead of liberal voters, who rushed to protest, poured money into Democratic campaigns and ran for local offices. This time, demonstrations have been minimal to nonexistent, as corporate leaders curry favor with the new administration and liberal celebrities mute their opposition out of fear of retribution.

The lack of public outcry has left Democrats debating whether liberals are simply tired of politics or whether they agree with more of Mr. Trump’s platform than they want to admit.

In Congress, several Democrats have expressed optimism that they can find ways to work with the new administration. They include some Democrats who mounted primary bids hoping to challenge Mr. Trump in 2020, including Senator Elizabeth Warren of Massachusetts and Ms. Klobuchar.

We cannot get caught up in every egregious thing he says, every insult he hurls, every ally he attacks and every executive order,” said Representative Veronica Escobar, Democrat of Texas. “There’s just too much.”

For others, letting Mr. Trump get away with things that violate their conscience is anathema to their political identity. Senator Christopher S. Murphy, Democrat of Connecticut, said he decided after Mr. Trump’s ill-fated attempt to freeze funding for trillions of dollars in federal grants and loans that he would not support any of the administration’s nominees or vote for any Republican priorities.

“It’s going to be very hard to mobilize people in America if we consistently deliver lots of votes for nominees and legislation,” Mr. Murphy said. “You have to portray a sense of alarm and urgency, or people will continue to believe that the country will be OK.”

But Representative Robert Garcia, Democrat of California, warned that presenting an alternate vision for the country could be more difficult given Mr. Trump’s alliance with leading social media and communications moguls.

“We’re not just up against Donald Trump. We’re up against the richest billionaires in the country who control much of our communication apparatus,” Mr. Garcia said. “We’ve got to start calling it like it is. And I think the American public and working-class people who make up a majority of this country will understand that.”