By Michael C. Bender and Aaron Zitner

WASHINGTON -- President Trump has long viewed his stewardship of the world's largest economy as his administration's defining legacy. With less than six months left to campaign, new polling shows he has few other advantages in his bid for re-election.

A Wall Street Journal/NBC News poll this week showed voters heavily prefer Mr. Trump to handle the economy despite the recession, while favoring former Vice President Joe Biden, the presumptive Democratic presidential nominee, on nearly every other matter that the poll measured, including whom they plan to vote for in November.

At this point in the 2016 race, the same poll showed Mr. Trump had an advantage over that year's Democratic nominee, Hillary Clinton, in several areas, including handling the economy, dealing with terrorism, changing business as usual in Washington, effectively getting things done and being honest and straightforward.

Tim Murtaugh, the Trump campaign's communications director, said the president's economic argument remains his overriding pitch, but he said voters will favor the incumbent on other issues as the contest unfolds and as he makes his case.

"The fact that this pandemic interrupted the economy actually makes the president's economic argument stronger," Mr. Murtaugh said. "Americans know he built the economy to great heights and can do it a second time."

Some campaign advisers have grown concerned about troubling polls for Mr. Trump, while others say plenty of time remains before Election Day, according to people familiar with the situation. The first five months of 2020 saw the threat of war with Iran, impeachment charges on which the president was acquitted, the coronavirus pandemic as well as a recession related to economic lockdowns, and peaceful protests and some unrest following the killing of George Floyd while in police custody in Minneapolis. The dynamics of the election could shift again before November.

Separately, the economy's importance to voters in the general election has changed since Bill Clinton's campaign team famously used the phrase "It's the economy, stupid" as an internal slogan for his successful 1992 campaign against George H.W. Bush. For the past several presidential elections, the influence of economic issues on how voters cast their presidential ballots has waned as partisanship has increased, analysts said.

"Over the last 12 years, it does appear that people's pocketbooks and the overall state of the economy matter less for their political choices, " said John Sides, a Vanderbilt University political science professor.

When asked to rank the most important problems facing the country, Americans in a recent Gallup survey prioritized poor government leadership, the spread of the coronavirus and the state of race relations ahead of the economy. That suggests Mr. Trump's handling of the economy won't be as much of a selling point to voters such as Rochelle Hofman, a 51-year-old high- school English teacher near Grand Rapids, Mich., who said she voted for Mr. Trump in 2016 but probably won't this year.

"President Trump has the knowledge and ability to help with the economy, as he has proven before," Ms. Hofman said. "But I'm very disappointed in his tweets and the things he says about various individuals, as well as groups. I think a lot of that is better left unsaid. I don't think that helps our country to heal."

In the latest WSJ/NBC News survey, Mr. Biden was favored over Mr. Trump by 5 percentage points on questions about who would end political gridlock and by 9 points on who would behave competently and effectively in the job. Mr. Biden had double-digit leads on questions of who would best handle the coronavirus pandemic, deal with health-care issues and address the concerns of minorities. Mr. Trump edged Mr. Biden on the question of who would be better at dealing with China, 43% to 40%.

While 54% of independent voters said they trusted Mr. Trump to handle the economy, a plurality of 45% to 35% said they plan to vote for Mr. Biden, suggesting that the president's strength on economic matters doesn't automatically translate into votes. In June 2016, independent voters trusted Mr. Trump over Mrs. Clinton with the economy, 43% to 19%, and a nearly equal share said they would support him for president. Independents accounted for 13% of voters in the new Journal survey, the same share as throughout the last presidential election year.

Despite the downturn brought on by measures to combat the pandemic, some voters view Mr. Trump as the best prospect to revive the economy.

Brad Bettencourt, a 31-year-old rental property owner who lives near Phoenix, said he credits Mr. Trump for the economy and will back him again. "I feel like there was a lot better growth when Trump was getting involved than when Obama was in there," Mr. Bettencourt said. "And Biden -- he kind of wants to play it as another extension of Obama's term."

Trump campaign officials say voters will become more focused on jobs, wages and other economic issues as the election approaches. They have discussed having Mr. Trump visit economically distressed areas. America First Policies, a pro-Trump group, is sponsoring a Great American Comeback Tour, which starts Friday as Vice President Mike Pence visits a manufacturing plant about 35 miles northeast of Pittsburgh to talk about reopening the economy.

Before the recession, Mr. Trump rarely missed a chance to remind the nation of the economy's strength, including when he welcomed children and their parents to the annual White House Easter Egg Roll in 2018 and at the national day of prayer service in May 2019, when he asked God to help Venezuelans who were starving, before noting a U.S. economy "that may be the best ever."

He has repeatedly said at campaign rallies that the low unemployment rate at the time was the only fact he needed to remember for the presidential debates.

"Let's say I'm on the debate stage and we start talking, and I say, 'Well, you know, we have the lowest rate ever for African-American, for Asian, for Hispanic,'" Mr. Trump said at a campaign rally in Louisiana last year. "All I have to do is say that and walk off the stage. I guess you win the debate. Who's going to beat you?"

He has sought opportunities to tout the economy since the slump, too. In the Rose Garden last week, in the midst of protests across the country for racial justice and against police brutality, Mr. Trump depicted the freshly released jobs report as a "tremendous tribute to equality." The jobless rate fell to 13.3% from 14.7%. Black unemployment ticked up to 16.8% from 16.7%.

"Hopefully, George is looking down right now and saying this is a great thing that is happening for our country," Mr. Trump said of Mr. Floyd, the man killed in Minneapolis. "This is a great day for him."

The economic argument in favor of Mr. Trump's re-election has become more nuanced, campaign officials said. Instead of talking about the strength of the economy, Mr. Trump must convince voters that he is best suited to lead a comeback, they said.

"We're going to have a very good third quarter, we're going to have a phenomenal fourth quarter," Mr. Trump said in a radio interview June 3. "And if I'm heading in that direction, I think we're going to be very hard to beat."

The Congressional Budget Office, a nonpartisan legislative agency, recently lowered its 2020-2030 forecast for U.S. economic output by $7.9 trillion, or 3% of gross domestic product, and said it doesn't expect to catch up to previously forecast levels until the fourth quarter of 2029.

Write to Michael C. Bender at Mike.Bender@wsj.com and Aaron Zitner at Aaron.Zitner@dowjones.com