WASHINGTON — President Biden enjoyed high approval among Americans in the early months of his presidency. Millions of vaccines were distributed throughout the United States. The White House trumpeted high job growth as proof of a rebounding economy.

But privately Mr. Biden’s lead pollster was already sounding the alarm that even with the early successes, certain gathering threats could sink support for the president and his party.

“Immigration is a growing vulnerability for the president,” John Anzalone and his team warned in a package of confidential polling, voter surveys and recommendations compiled for the White House. “Voters do not feel he has a plan to address the situation on the border, and it is starting to take a toll.”

Within a month, there was another stark warning. “Nearly nine in 10 registered voters are also concerned about increasing inflation,” said another memo obtained by The New York Times.

The series of confidential polling data and weekly memos presented to Mr. Biden’s inner circle from April of last year to January of this year provides a road map of the declining support of a president whose initial legislative proposals spurred comparisons to the New Deal or the Great Society.

Despite the early warnings from his pollster, Mr. Biden and his top advisers have struggled to prevent either issue from becoming a major political liability. His economic team said inflation was temporary. Turmoil among his immigration aides delayed any serious action to address the border.

For all the ambition of Mr. Biden’s domestic agenda, his pollster also warned him that most voters did not have a clear sense of his economic proposals. Starting last April, Mr. Anzalone urged Mr. Biden to do more to explain his plans for funding new government programs with new taxes on the wealthy. And last January, he wrote that “less than a fifth of voters report having heard a lot about” his climate and social spending package.

With congressional elections just months away, the polling memos underscore the biggest challenges for Mr. Biden and his party as they face the prospect of losing power to Republicans on Capitol Hill.

The correspondence was obtained in reporting for a forthcoming book, “This Will Not Pass: Trump, Biden and the Battle for America’s Future.”

Mr. Anzalone declined to comment. The documents were obtained from three people in the administration who had access to the polling data. They asked for anonymity because of the confidential and sensitive nature of the documents.

“The president has been focused on reducing costs for families and reducing the price of goods,” said David Kamin, the deputy director of the National Economic Council. He noted decisions to address “price pressures,” including forming a task force to address supply-chain issues and releasing millions of barrels of oil from a strategic reserve to counteract the economic impact of Russia’s invasion of Ukraine.

Chris Meagher, a White House spokesman, said the administration had been “consistent in our efforts to secure our border and build a fair, orderly and humane immigration system.”

Mr. Biden has blamed Russia’s invasion of Ukraine for high inflation, although consumer prices were high before the attack, and he pointed to lower unemployment as evidence of a rebounding economy amid the pandemic. The Homeland Security Department released a plan last week for how the administration would approach the border after lifting a Trump-era public health rule that empowered border agents to turn away migrants.

But those strategies have yet to resonate with voters, and the president’s own allies say unless the administration can find a way to address vulnerabilities outlined by his own team, Republicans will maintain momentum in November.

Just over half of Americans disapprove of the job Mr. Biden is doing, according to an average calculated by FiveThirtyEight, the data polling website. Inflation is at a 40-year high as the Fed considers raising interest rates. Moderate Democrats and Republicans are echoing Mr. Anzalone’s plea for a plan — more than one year later — to deter illegal crossings at the southwest border.

“Democrats have a really important choice to make. That is do you give into the fear-mongering that we know the right is going to play into or promote, or do you provide a vision of hope and prosperity for the future?” said Quentin James, the president of the Collective PAC, an organization dedicated to electing African American officials. “If we don’t, and we don’t provide a vision and a path forward, then folks will give into what they hear on the other side.”

When Mr. Anzalone sent the warning last spring that “immigration is the only issue where the president’s ratings are worse with our targets than with voters overall,” the Biden administration was struggling to move thousands of migrant children out of border facilities and into shelters.

His administration had a plan to address the root causes of migration in Central America and establish an orderly, compassionate system at the border, the president said. “But it’s going to take time,” Mr. Biden said during his first news conference as president.

Behind closed doors, his top aides debated throughout the spring and summer how fast to unwind Trump-era policies and what kind of system to replace them with. In July, even as the administration made progress in moving minors from the border facilities, Mr. Anzalone’s research showed the issue was causing anxiety among voters.

A memo on July 9 pointed to immigration and crime as two major weaknesses for Mr. Biden.

“President Biden continues to hold weaker, negative ratings on two hot-button issues that have been recently bubbling up,” Mr. Anzalone said.

Three days later, the president held a meeting on policing with Eric Adams, who would win the New York City mayoral election months later by making public safety a focus of his campaign. Mr. Biden has also encouraged localities to invest millions of dollars of coronavirus stimulus funds into police departments — an initiative that was unlikely to have an immediate impact on violent crime.

But the pollster warned that while the president’s performance on the coronavirus and the economy remained strong, “violent crime has edged out the coronavirus pandemic as the top crisis.”

Mr. Biden’s response to the pandemic maintained support among voters until the summer, according to the memos, when the withdrawal from Afghanistan and the spread of the Delta variant hurt his overall approval ratings.

The administration was surprised by the durability of inflation, despite Mr. Anzalone’s research, in part because the Delta variant’s impact on the economy had caused a prolonged stretch of spending on certain goods, rather than services, driving up prices.

But the administration maintained for months that inflation would be temporary, a message that has not resonated with voters, according to the research.

“The economy and inflation continue to dominate what is on the minds of voters — and their attitudes keep getting worse, which continues to impact the president’s job rating on the economy negatively,” one of the memos said. “And we should not expect positive movement in the short or mid-term as voters are not just feeling sour about the economy and inflation now, but voters also feel things are moving in the wrong direction for the future.”

Mr. Anzalone’s memos also presented research on what proposals voters supported.

His firm advised that describing infrastructure and social-spending packages as a means to address supply-chain issues, lower drug costs and tax the rich would be popular with older voters.

Mr. Biden appeared to capitalize on that research, holding various speeches on how his agenda was easing global shortages. His most recent budget proposal included a billionaires’ tax to ensure that the rich “pay their fair share.”