Mrs. Shaheen’s current 2-point advantage in within the margin of error, which was released Thursday.
“I feel very good because when I’m going out and about into people’s businesses, holding town halls — town halls are an important thing — and conveying my thoughts about being an independent voice for New Hampshire, it’s resonating,” Mr. Brown told WMUR.
Mr. Brown, a former U.S. senator from Massachusetts, moved to New Hampshire last December after losing his seat to Democrat Elizabeth Warren.
New Hampshire leans Democratic and Mr. Brown has been considered an underdog in the race. He got a boost from an endorsement last month from 2012 Republican presidential nominee Mitt Romney, who was governor of neighboring Massachusetts and has a summer home in New Hampshire.
Mrs. Shaheen has been dragged down by President Obama’s record low approval rating in the Granite State.
The Shaheen campaign says that the senator has a proven record of working for New Hampshire.
Mr. Brown still faces faces a Republican primary election Sept. 9 against former Sen. Robert C. Smith and former state Sen. Jim Rubens.
In the poll, both Mr. Smith and Mr. Rubens trailed by 14 points in a general election match-up against Mrs. Shaheen. She leads Mr. Smith 50-36 percent and Mr. Rubens 49-35 percent.