According to his own deadline, the New Jersey senator Cory Booker has less than two days to save his presidential campaign.

On Sunday he said an “avalanche of support” had brought him close to a self-imposed fundraising goal, but admitted he could be out of the race by Tuesday.

Some minor candidates have dropped out but the field is still unwieldy. On Friday the Democratic National Committee said its next debate, in Ohio on 15 October, would take place on one night. Twelve candidates, Booker among them, had qualified to appear.

Booker announced last week that if he did not raise an additional $1.7m by the end of September, he would quit the race. Since then he has raised about $1.5m. Asked on CNN’s State of the Union if the end was nigh, he said: “It could be.”

“But we’ve seen over the last week an avalanche of support. We have nearly 35,000 donors helping us make this goal, we’ve raised $1.5m plus, we’ve actually already crossed the threshold for the November debates of 165,000 unique donors.

“So the surge and the momentum’s great but, yeah, I still need help in this final 36 hours.”

Booker said he had set the fundraising goal in order to “stay in this race to win the nomination” as his candidacy was “not a vanity play or [about] ego”.

“I’m not going to be in this primary unless I have a viable path to win it,” he said.

The realclearpolitics.com national polling average shows how narrow that path has become.

Former vice-president Joe Biden leads from Massachusetts senator Elizabeth Warren, who has gained significant momentum. The Vermont senator Bernie Sanders is not far behind.

California senator Kamala Harris and South Bend, Indiana mayor Pete Buttigieg round out the top five, some distance back. Booker is ninth, behind the former Texas congressman Beto O’Rourke, former housing secretary Julían Castro and tech entrepreneur Andrew Yang.

The size of the field and the persistence of its stragglers is becoming a national talking point.

Returning this weekend for its 45th season, Saturday Night Live introduced a “CNN Impeachment Town Hall” in which “a muddled 10-person debate” was said to be the party’s choice for how to handle proceedings against Donald Trump.

Booker, played by Chris Redd, was not included among “the actual candidates”.

“We’re limiting the time you can speak by how well you’re doing in the polls,” the host said, “so Cory, you get five words.”

Redd offered: “Impeach Trump now because trouble.”

Asked if he would “like to leave now to beat traffic”, he said: “I would.”