Stephanie Cutter, a Democratic consultant who was President Barack Obama’s deputy campaign manager in 2012, said it was not atypical for an outsider like Mr. Yang — who has no background in politics — to command interest from a small but considerable portion of the electorate.

“There’s an appetite for the non-politician,” she said. “It doesn’t mean they make it over the finish line, but people are entertaining it at a marginal level.”

But as the debate season continues, the qualification criteria will only tighten, inevitably narrowing the field. At November’s debate, candidates will need at least 5 percent support in two polls in early-nominating states, or 3 percent in four early-state or national polls. (So far, just five candidates have hit the threshold, and three more are on the cusp.)

It is not unheard-of for candidates polling in the single digits to eventually seize the nomination. In fall 2003, Senator John Kerry often polled in the single digits, receiving as low as 4 percent in one nationwide CBS News poll; in the same survey, Senator John Edwards garnered only 2 percent. Mr. Kerry went on to become the Democratic nominee, and he chose Mr. Edwards as his running mate.

But Paul Maslin, a longtime Democratic pollster who worked on Howard Dean’s presidential campaign in 2004, noted that none of today’s single-digit candidates are polling as strongly in Iowa, New Hampshire and other early voting states as Mr. Kerry or Mr. Edwards were around the same time in 2003.

“I think the vast majority of primary voters are now realizing there’s only one of two or three possible winners,” Mr. Maslin said. “They have said to the vast majority of folks who are 3 percent or lower, ‘Thanks but no thanks.’”

As for the upcoming debate, he said, “Most of the Democratic primary voters would probably rather this be the last time you have that many people on the stage.”