In an interview on Friday, Mr. Elder said he was only about halfway to the donor threshold, and because his name is often omitted from Republican polling, reaching 1 percent could be impossible. For candidates like him, he conceded, making the stage is existential for his campaign.

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

Some candidates, like Mr. Pence and Asa Hutchinson, the former governor of Arkansas, could also fall short of qualifying. Mr. Pence, who has easily cleared the polling threshold but has badly lagged in fund-raising, launched an email blitz on Wednesday, pleading for 40,000 people to send his campaign $1. Mr. Hutchinson is still short of 40,000 but did reach 1 percent in a qualifying national poll this month.

Doug Burgum, the governor of North Dakota, may still qualify, in part because Mr. 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 is also pumping up his standing in early-state polls with a well-financed ad blitz.

“Gov. Burgum will absolutely be on the debate stage next month,” said his spokesman, Lance Trover.

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