In an interview Friday, Elder said he was only halfway through the donor threshold, and because his name is often omitted from Republican polls, getting to 1 percent might be impossible. For candidates like him, he admitted, making the stage existential for his campaign.

“It is crucial for me to be on that debate stage; that is Plan A, and Plan B is to make Plan A work,” she said, suggesting there is no other option.

Some candidates, like Pence and Asa Hutchinson, the former governor of Arkansas, also wouldn’t qualify. Pence, who easily passed the polling threshold but fell far behind in fundraising, launched an email barrage on Wednesday, pleading with 40,000 people to send $1 to his campaign. Mr. Hutchinson is still short of 40,000, but he reached 1 percent in a qualified national survey this month.

Doug Burgum, the governor of North Dakota, can still qualify, in part because Burgum, a wealthy former software executive, is offering $20 gift cards to the first 50,000 people who donate at least $1 to his campaign. He’s also boosting his position in early state polls with a well-financed publicity blitz.

“Gov. Burgum will absolutely be on the debate stage next month,” said Burgum’s spokeswoman, Lance Trover.

Mr. Burgum is not alone in his creative fundraising strategies. Mr. Ramaswamy, who like Mr. Burgum is wealthy enough to self-finance his presidential bid, is offering donors a 10 percent cut from the donations they get from those they convince to give to Ramaswamy’s campaign. Mr. Suárez last week he said he would enter anyone who sends his campaign $1 into a raffle for Lionel Messi’s first game with Inter Miami, the Major League Soccer club from South Florida.