Caroline Kennedy was meeting with upstate New York politicians Wednesday after publicly expressing interest in filling the U.S. Senate seat being vacated by Secretary of State-designate Hillary Clinton.

Kennedy, one of a dozen potential candidates for the post, benefits from popular name recognition and the political pull to meet with politicians and power brokers on short notice. She met Wednesday with Syracuse Mayor Matt Driscoll and Democratic Party bigwig John F.X. Mannion, among others.

The daughter of the late President John F. Kennedy and niece of the late Sen. Robert F. Kennedy, who held the seat in the Sixties, released a statement in which she said publicly for the first time that she "would be honored" to be considered for the appointment if Clinton is approved by the Senate and joins President-elect Barack Obama's Cabinet.

In Rochester, Kennedy stuck closely to a tightly controlled script but started to sound themes apparently designed to assuage those who question her readiness for a high-profile elected office.

"I just hope everybody understands that it is not a campaign but that I have had a lifelong devotion to public service," she said. "I've written books on the constitution and the importance of individual participation. I think I really could help bring change to Washington."

Before that, in Syracuse, her handlers cut her off when she was asked what her qualifications were to be a U.S. senator. As she left Syracuse City Hall, the first of her brief stops, she spoke briefly to a group of reporters and took no questions.

"I just wanted to say, as some of you may have heard, I would be honored to be considered for the position of U.S. senator," Kennedy said.

New York Gov. David Paterson, who is mulling his own political future, will select Clinton's replacement.

Kennedy's trip to upstate New York is similar to Clinton's "listening tour" in 1999 and 2000, when she first ran for the Senate. Like Clinton, Kennedy faces criticism because she's never been elected to public office. Some also worry that she would favor New York City interests over the rest of the state.

But it's Paterson who could have the most to gain from selecting Kennedy, who would fill out Clinton's term until the next general election in 2010.

The Democratic governor, who assumed power when former Gov. Eliot Spitzer resigned in a prostitution scandal, must also run for election in 2010. His choice for Senate could affect not only his popularity among New Yorkers, but also the fundraising strength of the state's Democratic ticket in 2010 and his relationship with the Obama administration.

At first glance, analysts and officials say at least two of these factors favor Kennedy, whose biggest challenger could be state Attorney General Andrew Cuomo, a former housing secretary in the Clinton administration and the son of former Gov. Mario Cuomo. Several other U.S. representatives and officials from the state have also expressed interest.

"There's a lot at stake in the governor's decision," said Lee Miringoff, director of the Marist Institute for Public Opinion. "[Paterson] may clearly look to someone who would provide some attraction to the ticket he would be on (in 2010), and also someone who would be able to raise him money."

On those factors, Miringoff said Kennedy would be a "huge pick" for the governor.

New York Assemblyman N. Nick Perry, the House Democratic whip, called Kennedy a "neatly packaged" candidate for the governor, who could bring in cash and "round off the statewide ticket" with a revered name among Democrats.

Perry said Kennedy would also be "tremendously helpful" to Paterson as he reaches out to the White House and Senate for federal support. (New York is facing severe fiscal problems; on Tuesday Paterson unveiled a tough plan to close the state's gaping budget deficit.)

"It would make our loss of Hillary Clinton so much less," Perry said.

Kennedy was an early Obama supporter during the Democratic primaries and helped lead his vice presidential vetting effort.

With her star power, Kennedy could hold unusual clout despite being one of the U.S. Senate's most junior members. Her appointment would also answer the calls of women's groups who want Paterson to pick a woman to replace Clinton.

U.S. Rep. Peter King, R-N.Y., who intends to run for the Senate seat in 2010, believes Paterson already has made up his mind.

"I'm guessing that he has decided on her," King told FOXNews.com. "If Barack Obama strongly wants Caroline Kennedy, certainly the governor has to factor that in ... It's hard to say no to a Kennedy."

But King joined skeptical Democrats in saying Kennedy brings little more to the job than a "famous name." King said Kennedy has no record.

While Kennedy is an accomplished author and education advocate, she never has served in public office.

Cuomo, on the other hand, was elected state attorney general in 2006 and previously served as U.S. housing secretary under President Clinton.

His name recognition and popularity in New York, as well as his ability to rake in money for the Democratic ticket in 2010, also cannot be underestimated. And Cuomo, after successfully running for statewide office, has ties to upstate New Yorkers that Kennedy does not.

A recent Marist Institute poll found that upstate and suburban New York voters favored Cuomo for Clinton's seat, while New York City voters favored Kennedy. Overall, the two were tied, at 25 percent each.

"A lot of people are still not sure about her," Miringoff said. "She needs very badly to establish some kind of policy focus with voters who at this point don't have a sense of that."

A Siena College poll released Wednesday found New York voters are divided over whether Cuomo or Kennedy should fill the seat and gave near identical approval ratings to both. But they said by a 31-16 percent margin that they believed Paterson will choose Kennedy. Thirty-eight percent said they didn't know or refused to answer, and 16 percent felt Paterson would pick someone else.

New York State Assembly Majority Leader Ron Canestrari, who is supporting Cuomo, told FOXNews.com that Kennedy is in "another realm" when it comes to star power, but his colleagues are genuinely split over whether to back Kennedy or Cuomo.

"[Cuomo] has been here with us through the good times, through the bad times, and produced as attorney general," Canestrari said.

There's one more factor that could lift Cuomo's chances. Cuomo ran unsuccessfully for the Democratic nomination for governor in 2002 but has been talked about as a potential candidate again in 2010.

By sending Cuomo to Washington, Paterson would eliminate that threat.

Cuomo could not be reached for comment.

Asked about Paterson's decision-making process, Buffalo Mayor Byron Brown -- another Democrat who is interested in Clinton's Senate seat -- said he's sure it will entail a "comprehensive vetting."

"He is a very thorough individual, a very serious-minded individual," Brown said. "I believe he will make a sound decision ... for the benefit of all New Yorkers."

Brown conceded that upstate voters have a "sense of confidence" in Cuomo, but he noted that Kennedy was moving to inspire that kind of confidence.

He said Kennedy, whom he described as surely qualified for the job, called him Monday to set up a meeting.

Kennedy has also retained the services of the political consulting firm, Knickerbocker SKD, which represents New York's senior senator, Charles Schumer.

Schumer would not endorse any candidate when asked about the seat Tuesday.

"All 12 of the candidates would be excellent," he told FOX News, adding that he's talked to Kennedy and she's "very interested" in the job.

FOXNews.com's Judson Berger, FOX News' Chad Pergram and Major Garrett and The Associated Press contributed to this report.