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.