PLYMOUTH, N.H. — Chris Pappas has been seen as Democrats’ presumed Senate nominee in New Hampshire since he entered the race more than a year ago.

And for most of that time, the four-term congressman has also been viewed as a slight favorite to hold the seat of retiring fellow Democrat Jeanne Shaheen in a state that hasn’t elected a Republican senator since 2010.

Democrats looking to flip the Senate have expanded the battleground map into red states such as Iowa and Ohio. But to win the majority, they’d need to hold their own seats like New Hampshire, where polls show a tight contest between Pappas and the Republican front-runner, former Sen. John E. Sununu.

Inside Elections with Nathan L. Gonzales shifted its rating of the race Thursday from Tilt Democratic to Toss-up.

“It’s a building block that Democrats can’t afford to toss aside,” Pappas said in an interview here last week. “If we can’t hold the Senate seat, then the math just doesn’t work in other states.”