But after scores of speeches and hundreds of votes, the short-statured councilwoman with a strong voice and gray, shoulder-length hair has only a few months left in her term, which ends in January.
Accompanied by her beloved pups Duncan, a McNab shepherd, and Harlo, a cattle dog, Mossar took time on a recent morning to reflect on her 10 years as one of the nine members of Palo Alto's governing body.
Known as a neighborhood activist, transportation advocate and environmentalist, Mossar began her political career by fending off rising Republican Duf Sundheim in 1997 to serve the last two years in Joe Simitian's council term, after he was elected to the Santa Clara County Board of Supervisors.
For Mossar, the hardest part of being a new council member, aside from the onslaught of new information, was learning to deal with the Brown Act, a California law that requires meetings to be public and governs the conduct of elected officials.
Council members are barred from most out-of-meeting discussions and from working together behind the scenes.
"The Brown Act makes you behave in ways you've never had to behave before. It's really weird not to work with other people on your (elected) body to figure out solutions," Mossar said, noting that working with a group was one of her strengths.
"It's a totally different role than being an advocate."
As a new council member, Mossar plunged into the historic preservation debate, quickly siding with preservationists in what she saw as an easy decision: "I think old buildings are wonderful. Ö I thought this was a no-brainer."
But now she counts that heated chapter of Palo Alto politics as one of her biggest mistakes.
Unaware of the depth of property owners' passions, Mossar said she eventually understood the other side of the issue, but by then tempers were raging.
"It's too bad we created such a furor. It takes a while to settle things back down and recover from that," Mossar said.
Re-elected in 1999 and appointed as mayor in 2003, Mossar's 2003 campaign was also marked by a bitter flier mailed out from the Palo Alto Firefighter's Union, which repeatedly referred to Mossar as "Mossa." That year Mossar was also criticized harshly by Councilwoman Nancy Lytle.
But Mossar prefers to discuss the city's accomplishments and changes in the workload of the council during her two-and-a-half terms.
She is particularly proud to have taken part in the creation of the Arastradero Preserve, the city's shuttle system and the Homer Avenue bike/pedestrian tunnel.
The city is also on stronger financial footing than it was a decade ago because of an increased realization that resources are limited, Mossar said.
The breadth of services — utilities, open space, branch libraries, a theater — offered by Palo Alto is unusual, even unique, but it is also costly, Mossar said.
Previously, spending was cyclical — "spend it when you got it and cut it when you don't," Mossar said.
Now, by setting aside money for current employees' medical expenses when they retire and making other "sustainable budgeting" decisions, the city's finances are more protected from the whims of lawmakers.
The need to plan ahead remains, Mossar said.
"I think the future is not just always rosy. I think it's going to be a struggle to maintain services."
Mossar has witnessed another systematic change in Palo Alto's civic process — the rise of the Internet, replete with anonymous online blogs and speedy e-mail.
The Web has "changed the face of politics," Mossar said.
Although more people can participate, no one has to make an effort to discuss issues or take the time to call a council member or attend a meeting, she said.
"Before the Internet, if they wanted to participate they had to show up to participate. Now, they can just send in their opinion and be unhappy when you don't select their choice in the end."
No one has figured out how to use the Internet meaningfully to work toward a political solution, Mossar said.
"I think it's a real problem for democracy," she said.
And it's made the job of council members much larger.
"When I was first elected you could spend 15 hours a week. Now, if you just spent 15 hours a week you wouldn't know what was going on."
As the race to replace Mossar and council members Judy Kleinberg, Bern Beecham and LaDoris Cordell heats up, Mossar said she is sad the number of women on the council will probably drop, as only two are running.
"Gender balance has been very important to good decision making," she said.
She disagrees with those who feel the council should have fewer members.
Council members serve on numerous regional committees and boards, she said.
"Palo Alto is a special community. It has a special intellect to it. I think the region and residents of Palo Alto benefit (from regional involvement)."
In addition, nine council members offer better representation of the citizens' diverse views and more refined debates, Mossar said.
"When you get down to five, the politics are much rawer. It swings much easier," she said.
Her advice for new council members?
"Just be patient and learn what you need to learn. Ö Understand there are a lot of things you don't know."
As for the oft-touted decline in civility, Mossar said it doesn't faze her.
"I had a pretty thick hide. You have to realize it isn't personal. It's about the job," she said.
But as her days as a council member dwindle, Mossar said she still hasn't decided what to do next.
"I vacillate between Ö never leaving the house or combing my hair, or getting a job lobbying legislators in Washington," Mossar said, half-joking.
"In fact, I just need a little break so I can settle in and focus."
Her current top interest is the rise in sea levels caused by global warming, particularly in the Bay Area.
Despite the interest in global warming, politicians and others haven't stopped pouring money into projects that may soon be under water, Mossar said.
"What people haven't really grasped is the problem exists today," she said. Constructing dikes around the entire Bay isn't feasible, but neither is letting some critical spots, such as San Francisco International Airport, go under, she added.
It's a multifaceted, long-range problem with no ideal solution, and it intrigues Mossar.
"I'm looking for a place to take that interest."
But then again, she may devote more time to art, a hobby she acquired rather recently after visiting museums and not understanding how the paintings had been made.
She's created pastels, made digital movies and plans to take a photography course in the fall.
"In a lot of ways I feel pretty open," Mossar said. "I have a lot of skills and a lot of interests, and I want to make sure I put them to the best use."