GREENFIELD, N.H. — The lawyer representing an adult-film actress who claims to have had an affair with President Trump stuck his toes deeper into electoral waters Sunday as he addressed about 200 people at a picnic held by New Hampshire Democrats.

Michael Avenatti told attendees at the Hillsborough County Democrats’ fund-raiser that the Trump presidency is “one large dumpster fire’’ and Democrats must fight “for the soul of our republic.’’

“In normal times, I would not be with you today. I would be back in Los Angeles enjoying my good fortune. But these — as all of you know — are anything but normal times,’’ said Avenatti, who represents Stormy Daniels and three other women who he says had relationships with Trump and were paid hush money before the 2016 presidential election.

Despite the outspoken attorney’s frequent appearances on cable news shows criticizing Trump, the pugnacious president has been uncharacteristically quiet about Avenatti, though he referred to Daniels as “a total con job’’ in a tweet that led Avenatti to file a defamation suit against the president.

Avenatti said in media interviews and Twitter postings on July 4 that he would run for president in 2020 if Trump seeks reelection and “if I think that there is no other candidate in the race that has a REAL chance at beating him,’’ and he has recently become a fixture at Democratic events.

Sunday marked Avenatti’s first appearance as a potential candidate in the state that holds the first-in-the-nation presidential primary.

Earlier this month he visited the Iowa State Fair, a traditional stop for candidates because Iowa’s presidential caucus precedes the New Hampshire primary.

He told reporters Sunday that he will visit Iowa again Wednesday and other states in coming weeks as he considers a potential run.

“I’m going to continue to travel around, and talk to people, and listen, and figure out what I’m going to do,’’ he said.

Avenatti said he was asked in Iowa if he was publicly contemplating a candidacy as a publicity stunt — a charge he called “offensive.’’

“I’m not going to go out and do this, and give speeches like this . . . on some lark,’’ he said. “I’m going to seriously consider this, because I think the 2020 election is a critical election. I would venture to say it’s the most critical in modern times.’’

In a polished stump speech, Avenatti drew on a biblical metaphor to describe Democrats.

“In the eternal battle of Davids versus Goliaths, we are the party of Davids,’’ he said. “We are the party of people who want to live their lives, chase their dreams, do their jobs, raise their children, leave the world a little better than they found it, and who so often find themselves up against Goliaths.’’

Those adversaries, he said, include “employers who don’t treat them right,’’ “an economy rigged to take the profits and the froth at the top and give it to the chosen few,’’ and “an outrageous immigration policy that seeks to strip children from families . . . in the interest of bigotry.’’

Avenatti said Trump is “the ultimate Goliath’’ and “when you are the party of Davids, you cannot afford to show up without a slingshot.’’

He told reporters that if he runs, he will wage an aggressive battle against Trump, matching the president’s bellicose style — much as he has while representing Daniels.

“I would do it the same way that I’ve done it over the last five to six months, although I think I’d even be more effective, were I to throw my hat in the ring,’’ he said. “There’s one thing I can promise you: Donald Trump doesn’t want to debate me on a national stage.’’

Avenatti said he thinks Trump is “a bully’’ who “doesn’t like people who punch back.’’

“I don’t think he’s very quick on his feet, I don’t think he’s that intelligent, and I think he’d be completely outclassed,’’ he said.

He also told reporters there is a “significant’’ chance Trump won’t seek reelection or even serve a full four-year term in office, depending on the outcome of special counsel Robert Mueller’s investigation into Russian meddling in the 2016 election and whether Democrats make big gains in Congress in November.

Avenatti’s message appeared to resonate with many picnic attendees, who welcomed him warmly with hugs, handshakes, and selfies and swarmed him again after his speech.

Joseph Smith, 73, a retired Army veteran from Amherst, N.H., said he thinks Avenatti is “a strong person intellectually. . . . I think he’s quite capable of dealing with Donald Trump. I like what he has to say.’’

His wife, Francie Smith, 69, a retired first-grade teacher, said she worries about Trump’s impact on the futures of their 13 grandchildren, particularly the seven granddaughters, if advances in women’s rights are reversed.

“I say often to my husband, ‘Think about what kind of a world you want those girls to be growing up in,’ ’’ she said. “Think of the Supreme Court.’’

Travis Andersen of the Globe staff contributed to this report. Jeremy C. Fox can be reached at jeremy.fox@globe.com. Follow him on Twitter @jeremycfox.