FARMINGTON, Conn. — As a pastor, Sam Saylor knows how draining the fight against gun violence can be. For years he attended vigils and comforted families until he could not take it anymore; he could not find the words for the grieving parents.

Then Mr. Saylor’s son Shane was killed, shot in the back as he tried to run from his assailant. Less than two months later, the shootings at nearby Sandy Hook Elementary School that killed 26 people, including 20 children, put the grimmest possible national spotlight on gun violence.

But minutes after speaking alongside Gov. Dannel P. Malloy and two members of the House of Representatives on Wednesday morning, Mr. Saylor could not conceal his impatience with Congress.

“Truthful?” he said. “We said, did it take Orlando for them to grow courage?”

House Democrats hosted 40 events across the country on Wednesday, with more than 60 members participating, trying to maintain the momentum created by their more than 25-hour sit-in on the chamber floor last week after the June 12 shooting at a nightclub in Orlando, Fla.

Scattered across their districts, the handful of committed but often wary activists who greeted them Wednesday served as a reminder of how difficult it can be to keep people energized when they have been disappointed for so long.

Just an hour’s drive from the site of the 2012 massacre at Sandy Hook in Newtown, Conn., Mr. Saylor and a few dozen others who favor gun restrictions joined Representatives Elizabeth Esty and Rosa DeLauro, Democrats of Connecticut, at a news conference at the University of Connecticut’s Health Center.

This state has become an emotional center of the gun control debate — and an example to those sick of waiting for Congress to act. In 2013, after Congress failed to restrict access to firearms, Connecticut enacted its own ban on many semiautomatic rifles.

It is a matter of identity for Mary Ellen Thibodeau of West Hartford. As she waited for Ms. Esty and Ms. DeLauro’s event to begin, Ms. Thibodeau, 66, described a trip to Costa Rica after the shooting in Newtown, where she was asked where she was from.

“We said, oh, Connecticut,” she said. “And they said, oh, Newtown. It was like, oh, that’s what we’re known for now. And that was really disappointing.”

Ms. DeLauro dismissed the idea that they were fighting a losing battle because of the nearly unanimous opposition from Republicans, who hold majorities in Congress.

“A vote ultimately may be unlikely, but I’m not going to concede that that is the point,” she said. “The fact of the matter is that we do have an opportunity.”

 Democrats are hopeful that the confluence of terrorism and guns in the recent Orlando shooting has been enough to draw a few more Republicans to their side. Last week eight Senate Republicans joined Democrats in keeping alive a “no fly, no buy” bill introduced by Senator Susan Collins, Republican of Maine.

Ms. Esty, who represents Newtown, argued that holding a vote would be to their advantage.

“If we were allowed a vote in the House of Representatives on comprehensive background checks, that would pass,” she said. “We have nearly 190 listed co-sponsors, bipartisan, and from conversations in back rooms, there are many Republicans who would vote for it if we were allowed a vote.”

House Democrats saw similar crowds at their events across the country after organizers of the sit-in called last week for a “national day of action” to be held on Wednesday. In Baltimore, several dozen people turned out for an event with four Democratic members of Maryland’s delegation, including Representatives Elijah Cummings and Chris Van Hollen, according to Mr. Van Hollen’s office. At a larger event in Chicago, several hundred people showed up for a rally with six House Democrats, Representative Jan Schakowsky of Illinois’ office said.

Not every event was so public, though. Representative Hank Johnson of Georgia met with activists at his Lithonia, Ga., office on Wednesday. Representative Ruben Gallego of Arizona held a conference call with reporters and local Arizona activists.

Mr. Van Hollen said Democrats are keeping all of their options open about what they will do when they return from the July Fourth recess next week.

“We have lots of options for making sure we do not return to business as usual until we have a vote on these common sense gun safety measures,” he said in a phone interview.

The protest in many ways started two weeks ago, when Senator Chris Murphy, Democrat of Connecticut, took to the floor in a 15-hour “talk-athon” with Senator Richard Blumenthal, his fellow Connecticut Democrat, among others.

And House Democrats reminded Republicans of their continued commitment to disruption on Tuesday, when a small group of lawmakers took to the floor during a “pro forma” session and, a largely symbolic protest.

Speaker Paul D. Ryan, Republican of Wisconsin, cautioned Monday that he would not allow the disruptions to continue.

“We will not tolerate this,” he said in an interview with the website wispolitics.com.

Despite the wariness of many supporters, the latest push feels like a breakthrough to others. Brandon McGee, a state representative in Connecticut, stood before several dozen people at a forum in Hartford hosted by Representative John Larson, one of the organizers of the sit-in, gesturing enthusiastically as he described what last week’s protest meant to him.

“That was monumental,” Mr. McGee said. “I think it started the new civil rights movement.”

But it also became clear that, in many ways, there is still a gulf among those who support more gun restrictions. Rev. Henry Brown, who was at both events in Connecticut on Wednesday, said he was dismayed that the organizers at the morning news conference in Farmington focused on mass shootings without discussing the violence their neighbors in Hartford grapple with daily.

“They didn’t even mention the violence that goes on in Hartford,” he said.

“If we are on the battlefield together, don’t you think there should have been some mention of what was going on in urban communities?” he continued. “It’s good that we’re talking about long guns, but the majority of our children are being killed by handguns.”

“Our babies die every day,” said Steve Harris, a retired firefighter and former member of the Hartford City Council, who was moderating the forum. “We have our Sandy Hook moment every day.”