But with Mr. Biden relatively low on funds and now trailing Ms. Warren in some polls in both of the first two voting states, Iowa and New Hampshire, his campaign faces the possibility of a serious pinch on his resources, long before the campaign expands to bigger states like California and Texas.

Tad Devine, a veteran Democratic strategist who advised Mr. Sanders’s 2016 campaign but is not working for anyone in the 2020 race, said the lack of cash would limit Mr. Biden’s political options. He pointed to the variety of areas where campaigns might want to invest money: airing television ads, deploying staff on the ground, staging splashy but expensive events and running a robust digital program.

“Your strategic options are limited,” Mr. Devine said, adding that the options available to Mr. Biden’s better-funded rivals were “much bigger.”

“He’s going to have to place the right bet,” Mr. Devine said. “It’s going to have to be a winner. It’s almost like you’re playing roulette, and one guy gets five numbers and the other guy gets one number. Who’s going to win?”

Over the summer, Mr. Biden had already begun to slash his digital spending budget, which was also clear in the new fillings. He spent about $1 million in the first half of the quarter and about $311,000 in the second half, records show.

During the quarter, Mr. Biden also spent $924,000 on a charter jet company, Advanced Aviation Team, as he raced across the country not only for rallies and speeches but also for dozens of fund-raisers on both coasts. Mr. Biden’s campaign said the costs included paying for carbon offsets.

Mr. Biden’s biggest expense is his payroll, which cost about $6.8 million in the past three months, records show. Mr. Biden had roughly 440 people on his payroll — about as many as Mr. Buttigieg — while Ms. Warren had more than 600 and Mr. Sanders had about 550.