ROCHESTER, N.H. — It was a Friday night in an ornate New Hampshire opera house, and Rep. Chris Pappas, the Democratic candidate for Senate here, had nearly finished his finely tuned stump speech.

He had slammed Washington corruption, promised to fight for affordable healthcare and lamented high prices, hewing to the message that Democrats across the country believe will win them back control of the Senate.

Pappas didn’t mention the man in plaid, standing amid the voters on the creaking wooden floor, who may nevertheless represent the most remarkable aspect of his candidacy: his husband.

Pappas, 46, is running a closer-than-expected campaign against former Sen. John Sununu, a Republican, a race that both parties view as critical. If he wins, he will be the first openly gay man to serve in the Senate — but this is not something he’s made central to his campaign.

“I’m not thinking much about history right now,” Pappas said in an interview.…