WASHINGTON—President Biden scrambled to cement his place at the top of the ticket amid deepening fissures in Democratic unity, with some in the party raising alarms that staying the course could ensure a win for former President Donald Trump and lead to a spate of down-ballot GOP victories in November.

Biden was scheduled to meet Wednesday night in the West Wing with Democratic governors. His chief of staff, Jeff Zients, is holding an afternoon all-staff call in a bid to boost flagging White House morale following the president’s disastrous debate against Trump. The Biden campaign is also holding an all-staff call on Wednesday afternoon.

The president is making a flurry of calls to Democrats to shore up support. He spoke to Senate Majority Leader Chuck Schumer (D., N.Y.) on Wednesday morning and had calls Tuesday with House Minority Leader Hakeem Jeffries (D., N.Y.) and Sen. Chris Coons (D., Del.), the White House said. Coons is a longtime Biden ally who occupies the Senate seat that Biden once held for more than three decades.

“The president is in this race to win it,” said Quentin Fulks, the Biden campaign’s principal deputy campaign manager, in an interview with CNN. “He is the Democratic nominee and from our perspective we’re going to continue to do everything we can to make sure that we’re building a campaign apparatus to reach voters.”

One day after the first Democratic member of Congress — Texas Rep. Lloyd Doggett—called on Biden to withdraw, other lawmakers were raising concerns about the fallout of the president continuing to be the Democratic nominee. Two Democrats from Trump-leaning districts, Reps. Jared Golden of Maine and Marie Gluesenkamp Perez of Washington, said they thought Trump would win the election if Biden were the nominee. Former Rep. Tim Ryan (D., Ohio) said Vice President Kamala Harris should replace Biden.

Biden

Rep. Lloyd Doggett of Texas has called on President Biden to drop out of the race. An undated handout photo provided October 11, 2022. U.S House of Representatives/Handout via REUTERS

Biden’s evening meeting is expected to include a number of Democratic governors attending in person, including California Gov. Gavin Newsom and Illinois Gov. J.B. Pritzker, both of whom are said to have national ambitions, along with other governors participating virtually. The meeting was organized by Minnesota Gov. Tim Walz, the chairman of the Democratic Governors Association.

Democratic lawmakers continued to raise deep concerns in private about Biden remaining on the ticket, and they said their worries are only increasing. Three lawmakers said they were hunkering down and waiting for Biden to either change course or for polling to come out that could make sticking with the president untenable.

“People are getting more worried,” one Democratic lawmaker said. Some have expressed anger at Biden’s team for, in their view, not being more forthright about the age-related issues that the president has been grappling with behind the scenes. “Everyone I’ve talked to is terrified. And very pissed at the Biden team,” another Democratic lawmaker said.

Meanwhile, Sabato’s Crystal Ball, a nonpartisan political-analysis group run by the University of Virginia Center for Politics, said Wednesday that Biden’s “debate performance was so bad that it has forced us to reassess some of our assumptions about the race.” The group projected that Michigan and Minnesota are now more competitive for Republicans.

Biden is scheduled Friday to hold a campaign event in Madison, Wis. The state’s Democratic senator, Tammy Baldwin, won’t join Biden at the Friday event, according to a spokesman for her campaign, who said she would be on a previously scheduled listening tour throughout the state.

While he is in Wisconsin, the president will tape an interview with ABC News’ George Stephanopoulos, a former Clinton White House aide who has been with ABC for more than two decades, as part of an effort by Biden’s team to counter the contention that his mental acuity is deteriorating.

Since the debate, several polls have shown a slight uptick in Trump’s support, but the contest is still tight. As of Wednesday morning, Trump led Biden by 2.1% in the FiveThirtyEight.com average of national polls.

In internal memos reviewed by The Wall Street Journal, Biden’s senior campaign officials played down the debate’s effect on public opinion. “Our internal battleground toplines from last night show a steady race: we estimate that we’re down just 1 point in margin. All of this is well within the margin of error and shows a steady race,” they said in a memo sent to Capitol Hill allies on Wednesday.

Natalie Andrews and Catherine Lucey contributed to this article.