"They want someone who can actually build the coalition we need to defeat him, because I think Trump is going to be a lot harder to beat than many Democrats think," he said of voters.
"That means a coalition that includes everyone in our party, plus independents, those Obama-Trump voters, and even some disaffected Republicans.
"I can build that coalition because I've built it in the most difficult circumstances before -- in the middle of a war."
The Massachusetts Democrat mentioned his service in the Iraq War, claiming his role as Marine platoon commander showed he can unite Americans from all walks of life.
"My fundamental job was to bring together this incredibly diverse group of Americans from all over this country, with different religious beliefs, different political beliefs, and get them united behind a common mission to serve America in the middle of a very divisive time: in the middle of a war that many of us disagreed with," he said.
"That's the leadership we need from the next president of the United States."
Moulton criticized the fact that Trump did not serve in Vietnam, instead receiving a deferment.
Baier noted that the lawmaker has called the president "unpatriotic" for the circumstance.
Moulton said he stands by that allegation.
"I think that if you lie to get out of the war, that makes you unpatriotic," he said.
"Especially, knowing that there's not like there is some empty seat with Donald Trump's name on it that went to Vietnam -- someone had to go in his place, some patriotic American who was willing to step up and to serve the country even in the midst of a terrible war so that no one had to go in his place.
"That doesn't make you a patriot -- to dodge service."
Moulton was not one of the 20 candidates invited to participate in this week's Democratic debates, which were to be held Wednesday and Thursday in Miami.