Senator-elect Hillary Clinton heads to Capitol Hill

WASHINGTON (CNN) -- It was her first day of orientation on Capitol Hill as a senator-elect, and first lady Hillary Rodham Clinton, soon to be sworn in as the junior senator from New York, arrived Tuesday with her own Secret Service detail.

"I've had a very good day," Clinton told reporters Tuesday afternoon as she and senator-elect Jon Corzine, a fellow Democrat from New Jersey, emerged from a late afternoon briefing on Senate history. "John and I have been going through orientation together."

Senator-elect Hillary Rodham Clinton talks to the press after orientation on Capitol Hill

While Clinton and the other new senators will not be sworn in until Jan. 3, their orientation began with a morning meeting and the traditional promenade before cameras and reporters at the U.S. Capitol. The first lady was prominent among her fellow freshman.

When asked about the best part of this first day of orientation, Clinton responded: "It's been the great privilege to be here, especially with the other new senators with whom I'll serve, all of whom are impressive and as committed as John and I are to the work ahead."

"I intend to work as hard as I can and to represent the people of New York to the best of my ability, to work hard to serve my constituents, to work with my colleagues wherever and whenever I can on behalf of our country -- so I am absolutely hoping to build relationships and create consensus with every senator," she added.

Although the first lady remains outwardly modest, Sen. John Breaux, a Louisiana Democrat who has been advising Clinton, acknowledged her special standing as a Washington veteran, even though she is a Senate novice.

"She'll know how to operate really well in the U.S. Senate. She comes in as a freshman, but she's not really a freshman," Breaux said.

"She's going to be well respected for her intelligence and her abilities and I think she'll fit in really well," he added. "She's a real work horse. I think she'll be very well received."

For the Democrats, Hillary Clinton represents a star politician who has already played in the big leagues.

"If I played baseball, and I used to, and somebody game me someone who could hit home runs, could hit singles, steal bases, and was a great defensive player, I'd say bring 'em on," said Sen. Harry Reid, a Nevada Democrat. "That's how I feel about Hillary."

Joining 12 other women now in an elite men's club, the star power of a first lady, the women say, will help their causes.

"Everybody talked about doctors being in charge of medical decisions, talked about schools and safety and equality for our children," said senator-elect Debbie Stabenow, a Michigan Democrat who defeated incumbent Spencer Abraham. "Now the question is, how do we follow through on that for the good of the country."

But although she may be a star among Democrats, the Republicans plan to treat her just like all the other rookies.

"She, I'm sure, is going to be a very diligent senator, work hard, get committee assignments where she has a real interest, and will be a very important part of this body just like every other senator is," said Sen. Trent Lott, R-Mississippi, the Senate majority leader.

CNN Correspondent Eileen O'Connor and Reuters contributed to this report