Challenger Michael Flaherty chases Mayor Thomas M. Menino to the big finish today with fence-sitting voters poised to hand the popular incumbent a decisive mandate or his spirited rival a historic political upset.

“The undecided (block of voters) leans against incumbency. The question is whether they get out to vote,” said Larry DiCara, a former mayoral candidate and City Council president.

But Joe Slavet, 89, a longtime City Hall observer, said that while Flaherty is a “hard campaigner,” he doubted he could overcome all the personal ties Menino has made with voters over the past 16 years.

“If a Flaherty upset happens . . . it would be one of the greatest upsets in the history of Boston elections,” he said.

A confident Menino said he had a comfortable lead but that he was not satisfied. “I’m real upbeat,” he said after trekking to a Norwood banquet hall to greet a group of West Roxbury and Roslindale seniors at a luncheon.

Leaving little to chance, he dashed from a dim sum breakfast in Chinatown to a book donation by Red Sox [team stats] infielder Kevin Youkilis [stats] at a Brighton school, stopped for coffee in Grove Hall and hosted a large rally in East Boston.

“I think the public, I hope they still have the appetite for a Menino administration,” the mayor said. “We all know the financial condition of this country. We need someone at the helm who understands how to run this city. I will give them a steady hand.”

Tag-teaming voters with his running mate, Sam Yoon, Flaherty made his case at a Dudley Square diner, outside a Dunkin’ Donuts in Jamaica Plain, at a supermarket in West Roxbury and a rally in Dorchester, insisting that Boston needs new leadership.

He got the vote of Donna Potter, 25, of Dorchester, a Dunkin’ Donuts worker who chatted with Flaherty while on break. “We need change. We’ve had him long enough,” Potter said of Menino.

But it is voters like Dominick Antonio, 61, a retired city parks worker from Jamaica Plain, who Flaherty hopes to sway. “I don’t know who I’m going to vote for. But I got a sneaky feeling it’s going to be an upset,” he said.

“We are going to make history. There is going to be a new mayor come tomorrow night,” said a buoyant Flaherty, noting his internal polls showed the race tightening, giving Menino only a 3 percent cushion, with as many as 10 percent of voters questioned undecided. Menino’s campaign declined to reveal its poll findings.

“That cuts our way,” Flaherty said. “If you have not decided already that you are going to return Mayor Menino for a 17th year, for a fifth four-year term, I think that bodes well for our message that we have a plan to fix the schools, make the streets safer and to fight to put people back to work.”

Menino said last night that his tracking shows some 15 percent undecided voters, a “good number” of whom are breaking his way. He led backers at an East Boston social center last night in a chant of, “Four more years!”