Senator Manchin is railing against partisan politics in New Hampshire after a busy week for a third-party group, No Labels, which is aiming at putting up a candidate to run alongside the widely anticipated rematch of Presidents Biden and Trump.

“The people who are just telling me I’m going to vote for the Democrat because I’m a Democrat, I’m going to vote for the Republican no matter who it is — that’s bullcrap — vote for the person, vote for the best person that should be leading this country,” Mr. Manchin said.

A former governor of Massachusetts who attended the event, Bill Weld, tells the Sun that Mr. Manchin should “absolutely” run on the No Labels ticket.

“I would love it if he would,” Mr. Weld says. “Obviously I’m a bad person to ask about the duopoly because when I ran as a  Libertarian, the duopoly in Washington — only Republicans and Democrats — was our enemy no. 1.”

A Republican strategist at the event, Matthew Bartlet, expressed doubt about a potential No Labels bid, telling the Sun, “It’s all well and good to hear calls for civility and moderation in politics, but let’s just be real: For the better part of two years, Joe Manchin was the most powerful person in the United States, even more powerful than Joe Biden.”

Mr. Bartlett added, “It’s unclear what more he would want or need or be able to do in a different role or if he wants to seek that role. … We have yet to see just a coherent third-party plan from Joe Manchin or anyone at this point.”

The senator stressed that he hoped Mr. Biden would turn toward what Mr. Manchin sees as the political center in America, saying, “I’d love to see President Biden move back to where he came from.”

Mr. Manchin went on to tout recent accomplishments like the Inflation Reduction Act and policies passed over the past few years, such as lowering prescription drug prices in America.

When asked about the likely decision voters will face in November, between Messrs. Biden and Trump, Mr. Manchin said that “you have to make a decision” and look at the character of the candidates.

Mr. Manchin’s speech in New Hampshire comes after a week of activity for the No Labels organization. On Thursday, Governor Hogan of Maryland resigned from the board of No Labels.

The resignation came with little explanation other than a letter from December that was obtained by the Associated Press. The move could open the door to a potential presidential bid from the former governor on the No Labels ticket.

“In stepping aside, it is my intent that new leaders, who can devote themselves full-time to the effort, will be able to take the helm to direct the No Labels political operation,” Mr. Hogan wrote.

On Wednesday, officials in Maryland, the state where Mr. Hogan served as governor, also announced that No Labels had surpassed the signature requirements to appear on ballots there, bringing the total number of states in which the organization has obtained ballot access to 14.

The New York Times also reports this week that a super PAC aiming to support the eventual No Labels candidate plans to file paperwork imminently.

The group said that it had $2 million in initial commitments but expected up to $300 million in contributions to the efforts should No Labels settle on a “viable” ticket.

The Sun’s Caroline McCaughey contributed reporting to this story.