President Joe Biden has held his ground against Republican presumptive nominee Donald Trump despite questions about Biden’s mental fitness and calls for him to quit the 2024 race, according to the latest PBS News/NPR/Marist poll.

If the election were held today, 50 percent of U.S. registered voters said they would support Biden, while 48 percent said they would vote for Trump, the difference between the two falling within the margin of error.

Yet, a majority of Americans believe that Trump will win the election in November. And more than half think that neither Biden nor Trump should lead their respective party’s White House tickets this year.

“We have a race that didn’t change much,” said Amy Walter of the Cook Political Report with Amy Walter. “If you’re Biden, this poll suggests you’re in fine shape to continue.”

Though it’s been a fraught election cycle for both presumptive nominees, turbocharged in recent weeks by Trump’s felony conviction and Biden’s muddled debate performance, these sentiments have remained virtually unchanged for nearly a year.

“The survey shows that President Biden can still win this election, he just needs to convince Democrats — including those inclined to vote for him — that he can,” said Navin Nayak, president of the Center for American Progress Action Fund. “Based on this survey, what’s most important is the actual vote hasn’t changed since the debate, but there’s a crisis of confidence among Democrats that the president needs to address.”

The growing number of calls from Democratic lawmakers and donors for Biden to step aside in the 2024 race has fueled speculation about alternative candidates for the top of the party’s ticket over the last two weeks.

Nearly two-thirds of Americans say Biden does not have the mental fitness to serve as president, while about half question Trump’s acuity, according to this latest poll. At the same time, a majority of Americans say Trump does not have the character to serve as president. About half of Americans say Biden has the character to lead the nation.

Overall, 59 percent of Americans think Trump will win in November, including nearly all Republicans, a majority of independents and nearly a quarter of Democrats.

At a Thursday news conference marking the end of the NATO summit in Washington, a reporter asked Biden whether he was concerned about damaging his decadeslong legacy in politics by choosing to stay in the race despite voter concerns.

“I’m not in this for my legacy. I’m in this to complete the job I started,” said Biden, who repeatedly doubled down on his commitment to stay at the top of the ticket.

In head-to-head comparisons against Trump in this poll, none of a given handful of other Democrats surpassed Biden’s razor-thin lead, and all of them fell within the poll’s margin of error. This survey did not attempt to include all possible contenders, but U.S. registered voters were asked about several prominent Democratic leaders.

How would other Democrats fare if Biden steps aside?

If the election were held today and Vice President Kamala Harris was the Democratic nominee running against Trump, 50 percent of respondents said they would vote for her, while 49 percent said they would vote for Trump.

“I wouldn’t have picked her if I didn’t think she was qualified to be president,” Biden said of Harris at the NATO news conference late Thursday.

Gavin Newsom, the Democratic governor of California, has also been floated as a potential contender. In this latest poll, 50 percent of voters said they would choose him if he were the Democratic Party’s presidential nominee, while 48 percent stood with Trump.

If Democrats instead went with Michigan Gov. Gretchen Whitmer, who chairs Biden’s reelection campaign, 49 percent of voters said they would back Whitmer. At the same time, 49 percent said they would support Trump. Whitmer has remained adamant that she stands by Biden and told the PBS News Hour’s co-anchor Amna Nawaz that Biden “has delivered for people.”

Chart by Jenna Cohen/PBS News Hour

Republican strategist Sarah Longwell said it is “absolutely not” too late for Democrats to pick someone else to lead their party’s ticket as they prepare for the Democratic National Convention in Chicago in August.

“Four months is a lifetime,” she said of the run-up to the November election, pointing out that neither Biden nor Trump are officially nominated yet.

For people who want to see someone other than Biden in the race for the White House, Walter said this latest poll “has something good for you.” Other contenders don’t appear to do better than Biden, but they also don’t do worse.

“If tomorrow I show up at the convention, and they say they want someone else, that’s the democratic process,” Biden said Thursday before whispering, “But that’s not going to happen.”

The 56 percent of Americans who say Biden should not lead the Democratic Party’s bid for the White House includes a sizable minority of Democrats (40 percent), in addition to 61 percent of independents and 68 percent of Republicans. Younger Americans are more likely to feel this way than older Americans, according to this latest poll.

Similarly, 54 percent of Americans say Trump should not be the Republican Party’s candidate in the 2024 presidential election. Younger Americans, especially those ages 18 to 29, were divided over whether or not Trump should be in this race. No serious contenders are in view for Trump, who will be formally named his party’s nominee for president next week during the Republican National Convention in Milwaukee.

Mental fitness and character

Biden’s performance during the June 27 presidential debate against Trump prompted concerns that he may be mentally unfit to serve a second term in the White House.

Chart by Jenna Cohen/PBS News Hour

“So much about Biden and Trump is baked in,” Walter said. “The real concern among Democrats — it’s not that there’s something new people will learn about Biden, but [that] what we saw on debate night is going to happen again. That’s the risk.”

Earlier this week, a Cook Political Report analysis of new polling data showed more voters in key battleground states leaning away from Biden after the debate.

WATCH: New polls show Biden slipping further behind Trump in critical swing states

“I think voters got a lot of new information from that debate,” said Longwell, who noted that the will of primary voters who had cast their ballots for Biden would not be diminished if Democrats switched to a different nominee.

“If Joe Biden had a health event and had to step aside, nobody would say, ‘Oh, the voters voted for him,’” she said. “They would say, ‘Oh, he had a health event.’”

In May, Trump became the first former president in U.S. history to be convicted of a felony and continues to be the focus of multiple ongoing criminal and civil investigations, including allegations that he worked to overturn the 2020 presidential election.

In spite of these historic developments, just as many Americans say they have a favorable impression of Biden as they do Trump, at 43 percent for each candidate, a number that has largely held steady for much of the past year.

Who will win, according to Americans right now

Younger Americans were more likely than older Americans to think Trump stands the best chance of securing a second term as president in the current race. In this latest poll, 62 percent of adults ages 18 to 29 said Trump was most likely to win the election, significantly more than 55 percent of adults age 60 or older.

Meanwhile, 39 percent of Americans believe Biden will return to the White House, including about three-quarters of Democrats and more than a third of independents.

Looking at voter enthusiasm, 9 in 10 U.S. registered voters say they plan to vote in November.

PBS News, NPR and Marist Poll conducted a survey on July 9 through July 10 that polled 1,309 U.S. adults with a margin of error of 3.1 percentage points, 1,174 registered voters with a margin of error of 3.3 percentage points and 954 registered voters who definitely plan to vote in November’s general election with a margin of error of 3.6 percentage points.