Democratic frustration and worries were growing on Wednesday as Graham Platner hung on to the party’s nomination for Senate in Maine nearly 48 hours after a woman accused him of rape.

Despite losing every prominent ally and major sources of party funding, Mr. Platner has seemed to hold out hope of influencing the choice of his replacement in the state’s crucial Senate race.

The Maine Democratic Party, which is facing a Monday legal deadline for him to drop out so it can pick a new nominee, has insisted he will have no say.

Mr. Platner plans to join a campaign staff call on Wednesday night and is expected to release a video indicating his path forward, according to a person briefed on the plans who spoke on the condition of anonymity to discuss the internal campaign discussions.

If Mr. Platner ends his bid, Maine Democrats face the daunting prospect of crunching down what would normally be a monthslong primary campaign into a rapid-fire nomination process by July 27, just under three weeks from now. Democrats are trying to unseat Senator Susan Collins, a longtime Republican, in a race widely viewed as one of the most important midterm contests.

“He needs to drop out so that the party and the voters of the state can move forward,” said David Farmer, a Democratic consultant in Maine. “The party can’t do anything until he withdraws.”

The conflict between the state party and Mr. Platner raged through Wednesday afternoon, when his campaign texted hundreds of volunteers asking for their feedback on the nomination process.

The campaign, which had denied in a statement on Tuesday night that it was trying to influence who would replace Mr. Platner, said it would collect responses for “the next 48 hours,” raising new questions about a timeline for his withdrawal.

“If the Democratic Party hopes to harness our movement,” Mr. Platner’s campaign manager, Ben Chin, wrote in the text, “it must consult the feedback and proposals of the people who built and sustained this.”

Minutes later, Devon Murphy-Anderson, the executive director of the Maine Democratic Party, said the party was “frustrated with Graham Platner’s continued efforts to manipulate this process” and assailed his campaign for “distracting from the job of defeating Susan Collins in November.”

But Ms. Murphy-Anderson — who a day earlier had released a direct-to-camera video declaring that Mr. Platner would have “no role” in the selection process — added that his supporters were “a vital part of our Party and deserve to participate in an open process to select Platner’s replacement.”

Many Democrats expected that Mr. Platner would drop out soon after Jenny Racicot accused him of sexually assaulting her in a Politico report published on Monday afternoon.

But some Platner allies moved to canvass national Democrats to assess whether he still had support. Former Senator Barbara Boxer of California said that a representative from the campaign reached out to her on Monday afternoon to see whether she would stand with Mr. Platner.

She refused.

As the party quibbles with Mr. Platner, several Maine politicians have begun jockeying for the nomination, including some who lost primary races in June for governor and for Maine’s Second Congressional District.

And major party figures are starting to push for influence. On Wednesday, Representative Ro Khanna of California — a former champion of Mr. Platner’s who has called on him to withdraw — endorsed Troy Jackson, a fellow progressive who came in third in the Democratic primary for governor in June.

Prominent figures in the state have had to quell speculation about a run, including the actor Patrick Dempsey of “Grey’s Anatomy” fame and Heather Cox Richardson, a historian and author of a popular political newsletter. A spokesman for Representative Jared Golden of Maine, who holds the most Republican-leaning seat of any Democrat in the House, told The New York Times on Tuesday night that he “would have put his name forward many months ago” if he wanted the nomination.

State law does not determine how the nomination process would work, but the options being discussed include a convention of hundreds of state party delegates or a statewide caucus in late July, both of which would require herculean efforts to coordinate on short notice.

The Maine Democratic Party planned to hold an emergency meeting with members at 4:30 p.m. on Wednesday, its chair, Charles Dingman, said.

Democrats are losing ground with every day that goes by, as donors withhold support until the situation becomes clearer. A virtual fund-raiser for Mr. Platner that was scheduled for Thursday was canceled this week, co-hosts told The Times.

Morris Pearl, the president of a group of Democratic donors who supported Mr. Platner, said he hoped the party would choose someone who “has a similar ideology of economic justice and doing something to help people, but who, you know, does not have this more or less fatal flaw.”

“I’m kind of upset,” he added, “but I can’t find anyone to be upset at besides Mr. Platner.”

Reporting was contributed by Tim Balk, Kellen Browning, Katie Glueck and Reid J. Epstein.