At a moment of deep, factionalizing partisanship, when congressional Republicans were unable to find a consensus candidate who wanted to become speaker of the House of Representatives, the nonpartisan group No Labels tried an experiment in New Hampshire.

The group, led by Jon M. Huntsman Jr., the former governor of Utah, and Joseph I. Lieberman, the former senator from Connecticut, invited presidential candidates from both parties to speak at a daylong “Problem Solver Convention” in Manchester on Monday. Just showing up at the conference was deemed proof of being one of those so-called problem solvers, even if the speeches there did not always focus on big ideas.

The event, on live video, drew eight presidential candidates from the field of more than 20 Democrats and Republicans. Founded on the idea that toxic political divisions are ruining the nation, officials with No Labels have long advocated focusing on fixing government instead of partisan politicking.

For candidates whose speeches use the language of outrage, such as Donald J. Trump, the No Labels event had the potential to be an odd fit.