“It seems like anytime Donald Trump feels threatened by a strong woman, he lashes out with this gross, weird attack,” her communications director, Lily Adams, wrote the next day. “It’s the kind of sexism that makes me want to run my head through a wall. But instead of doing that, let’s do something productive. I know we’ve asked a lot lately — but can you step up and add a donation to Kamala’s campaign today?”

A month later, Ms. Gillibrand did the same after a tense exchange on Fox News, in which she denounced Fox’s coverage of abortion and the moderator suggested she was being rude.

“The suffragists sure as hell didn’t make change by worrying about being polite,” Ms. Gillibrand wrote two days later. “I promise you I’ll be this brave and this fearless from the Democratic debate stage, too — but I need your help to guarantee I’ll be there.”

Some of the lowest-polling candidates, always looking for a breakthrough moment, have seized on almost any public mention as evidence that opponents are terrified of their “momentum.”

“BREAKING: The GOP just attacked Seth,” an email from Mr. Moulton’s campaign declared June 3, citing a tweet of the sort the Republican National Committee posts about any Democratic candidate who goes on TV. “Rush $10 — Click here to fight back against the GOP attacks. Maggie, the GOP and their wealthy donors are scared of Seth.”

You’ve never seen so much hyperbole.

Several candidates hovering near 1 percent in the polls have declared that one survey or another showed them in the “top 10.” In most cases, what they meant was that fewer than 10 people had more than 1 percent support, leaving a large cluster of marginal contenders tied for, say, ninth place.

By this standard, in many polls, 15 or more candidates can claim to be in the top 10.

Hyperbole is also popular in subject lines. “INCREDIBLE news” can mean, as it did in an email from Mr. Bennet’s campaign May 18, “Michael only announced his candidacy two weeks ago but he’s already met the polling threshold in two of the three qualifying polls he needs!!!” (The threshold is 1 percent, and one of the polls had been released more than two months earlier.)