Democrats could hardly believe their good fortune last month when it became clear that Hillary Clinton was headed to a general election showdown with Donald J. Trump. Mr. Trump carried so much baggage and had insulted so many voting blocs that some Clinton supporters began to imagine a landslide.
But early optimism that this would be an easy race is evaporating. In the corridors of Congress, on airplane shuttles between New York and Washington, at donor gatherings and on conference calls, anxiety is spreading through the Democratic Party that Mrs. Clinton is struggling to find her footing.
While she enjoys many demographic advantages heading into the fall, key Democrats say they are growing worried that her campaign has not determined how to combat her unpredictable, often wily Republican rival, to whom criticism seldom sticks and rules of decorum seem not to apply.
Mrs. Clinton is pressing ahead with a conventional campaign, echoing the 2012 themes used against the Republican nominee that year, Mitt Romney. But Mr. Trump is running a jarringly different crusade: accusing her husband, former President Bill Clinton, of rape; proposing that the country conduct brutal methods of torture; and suggesting that South Korea and Japan be permitted to develop nuclear arms. Prominent Democrats say a more provocative approach is needed.
“The guy’s a maniac,” John Burton, the chairman of the California Democratic Party, said about Mr. Trump. Referring to a famous 1964 political message, he said, “You could run the old L.B.J. ad against Goldwater, with ‘Three, two, one,’ and a hydrogen bomb blows up with a little girl counting daisies.”
Of course, Mr. Trump faces many hurdles himself, and has stumbled in managing his growing campaign as he shifts toward a general election. But Democrats suggest that the past few weeks have shown that Mrs. Clinton and her aides must become more agile and creative against him.
The sense of nervousness crystallized this week when Mrs. Clinton devoted campaign events across California to hitting Mr. Trump for not releasing his tax returns and depicting him as a cold corporate titan who profited off the housing crisis. Such charges helped undermine Mr. Romney four years ago. Yet Mrs. Clinton’s remarks received little in-depth coverage in the news media, while cable channels went live with Mr. Trump’s rat-a-tat recitation of “Crooked Hillary,” his favored nickname for her.
Ken Salazar, the former Colorado senator who has been mentioned as a possible Clinton running mate, said the campaign should draw a sharp contrast between Mr. Trump’s shortcomings and Mrs. Clinton’s potential to be “the most qualified person to be president in our lifetime.”
“The campaign needs to expose Donald Trump as the opposite — selfish, egomaniac, divisive and unqualified to be president,” Mr. Salazar said in an email.
Jennifer Palmieri, a spokeswoman for the Clinton campaign, said that the news coverage Mr. Trump is receiving is not helping him. She said that unlike Mr. Trump, who uses “nothing but his own mouth,” Mrs. Clinton has a campaign that employs many methods of communication, including videos, respected surrogates and bilingual outreach. “We hear from friends who think we should act more like Trump or criticize us for sometimes using traditional communications tactics,” she said. “But we don’t think that’s the answer.”
As a candidate, Mrs. Clinton is not without her own issues to overcome, including her inability to quickly put away Senator Bernie Sanders and her use of a private email server when she was secretary of state, feeding a perception she is not trustworthy. In a report delivered this past week to Congress, the State Department’s inspector general strongly criticized her for the practice.
Senator Chuck Schumer of New York is concerned that she lacks a comprehensive strategy to confront Mr. Trump, and has told Democrats that the Clinton campaign must bring on a senior staff member dedicated only to the Trump portfolio.
“As soon as she clinches the nomination, we need a high-level person in the campaign whose sole job is to respond to Trump, almost on an hourly basis,” said Mr. Schumer, who has begun conversations with Clinton officials about who could fill that role.
During a conference call this month, high-profile female supporters pressed Mrs. Clinton’s advisers about her message — which has as a slogan “Breaking Down Barriers” — and whether it needs to shift for the general election. “The message will be broadening,” Karen Finney, a senior adviser, explained, according to a transcript of the call obtained by The New York Times. “But,” she added, leaving some participants perplexed, “breaking down barriers and unity will continue to be part of the theme because Hillary believes we need to come together as a country in many ways.”
Debates have broken out in Mrs. Clinton’s Brooklyn headquarters over the best approach to take. Some advisers worry that by running against Mr. Trump as she would a traditional Republican candidate, Mrs. Clinton is actually making the reality-television star appear more legitimate.
This month, when Mr. Trump suggested he would reduce the national debt by negotiating with creditors to accept something less than full payment, economists dismissed the idea as fanciful.
Hours later, the Clinton campaign sent out a news release about Mr. Trump’s “risky” idea of defaulting on the national debt with a response from Gene Sperling, formerly a senior economic adviser to both President Obama and Mr. Clinton, condemning the idea.
The seriousness of the campaign’s response seemed to elevate a nonsensical proposal. “That is a danger,” said Dan Pfeiffer, a former senior adviser to Mr. Obama. “You have to take the threat of Trump becoming president seriously, but you shouldn’t treat him as a serious person.”
At the same time, Mrs. Clinton’s attempts at poking Mr. Trump have felt tame compared with what he has unleashed. The day after he accused her husband of rape on Fox News this month, she told CNN, “I have concluded he is not qualified to be president.”
Her aides were exuberant that Mrs. Clinton, a cautious candidate who for weeks had demurred when asked if Mr. Trump was up to the job, had finally publicly declared him unfit. But to many Clinton allies, it felt like a tepid tactic from yesteryear.
“Sometimes, you get the feeling that they’re in a professional boxing match and he’s in a street fight, and they’re coming in with their gloves on,” said the Rev. Al Sharpton, expressing dismay over the Clinton operation’s apparent lack of appetite for combat.
“This is a street fight with a guy with a razor and a broken Coca-Cola bottle,” he added, “and you’ve got to fight him like that.”
Ms. Palmieri said, “Each tactic we use is designed for a particular purpose to either engage the press or reach a certain audience.”
Any aggressive approach by Mrs. Clinton is potentially dangerous, however, because recent polls show she is viewed negatively by a majority of the electorate.
The campaign says it intends to go after Mr. Trump more forcefully, particularly on national security and his business record, after June 7, when Mrs. Clinton is expected to officially clinch her party’s nomination.
For now, her aides appear to be throwing ideas against a wall to see what sticks, including trying out different monikers after the Democratic National Committee’s “Dangerous Donald” flopped. An internal favorite is “Poor Donald,” with its implication that Mr. Trump, famously defensive about his net worth, is not nearly as wealthy as he lets on.
Her advisers also say that a large percentage of voters have not yet paid attention to the details of the race and do not know about Mr. Trump’s business dealings or that he has refused to release his taxes.
“It wouldn’t be a general election without some early bed-wetting from Washington insiders,” said Robby Mook, Mrs. Clinton’s campaign manager. He noted that the campaign had attacked Mr. Trump over the tax returns and for his “demeaning millions of Americans.”
“Our campaign has already shown the resolve to take him on and put him on defense in ways his Republican challengers never could,” Mr. Mook added.
William M. Daley, Mr. Obama’s former White House chief of staff, attributed any early shortcomings in taking on Mr. Trump to Mrs. Clinton’s prolonged primary battle against Mr. Sanders. The period between the June 7 contests and the July convention will reshape the race, he said.
To that end, Joel Benenson, Mrs. Clinton’s pollster and chief strategist, pointed out that at this stage in the 2008 primary battle against Mrs. Clinton, Mr. Obama led Senator John McCain by only two percentage points. He went on to defeat Mr. McCain by 7.2 percentage points.
It is clear, however, that Democrats are no longer mocking Mr. Trump. Many of them seem determined instead to understand his appeal.
In an interview on Friday, Gov. John Hickenlooper of Colorado said he had purchased and begun reading Mr. Trump’s book “The Art of the Deal.”
The governor said he remained confident that Mrs. Clinton would ultimately win, but added that “she has to be careful, because now he has momentum.”