In fact, a new CBS News poll shows Clinton holding a over Sen. Barack Obama among Democratic voters.
"It will be a great contest with a lot of talented people," Clinton said Sunday – "a lot" being the operative word.
Clinton told CBS Evening News anchor Katie Couric on Monday that she is proud of her husband's White House record and wants to build on it.
"I could go on for a long time about all the good things that were done for the country and America's position in the world during the eight years of my husband's administration," Clinton said. "And I would like to get back to building on what works … recommending the kind of bold, but practical changes – like universal health care, like energy independence – that were not possible in the first Clinton administration."
Iraq may be one of the biggest issues on the campaign trail, and Clinton reiterated to Couric that she opposes the "escalation the president has proposed."
"Unfortunately, the fact is he is carrying out the policy. He already had in motion the movement of troops into Iraq," Clinton said. "What we're trying to do is send a bipartisan message, if possible, that we disapprove of this escalation, that we want to begin a phased redeployment that I have called for more than a year and a half – that we want to get our troops home as soon as possible."
In her first appearance after Saturday's announcement, New York's junior senator upstaged two other contenders who announced their entry into the race: , a fellow Democrat, and , who admitted his quest for the Republican nomination is something of a fantasy.
"My family and I are taking the first steps on the yellow brick road to the White House," Brownback, R-Kan., said at a rally in Topeka.
It might be easier to get an audience with the Wizard of Oz than steal Clinton's thunder right now. Whether Democrat or Republican, others seeking the job found themselves scrambling to acknowledge her dominance without coming across as irrelevant.
"I think she's incredibly formidable and has got to be the front-runner and the odds-on pick right now," Sen. Joe Biden, D-Del., said Sunday.
"I think she'd be a very formidable candidate," Sen. John McCain, R-Ariz., said.
At this point, only McCain polls in the high 40s with Clinton. That's with 22 months to go before the election and a lot of unknowns ahead, including the staying power of Barack Obama, the young Illinois senator, who's currently Clinton's closest Democratic rival.
But as the presumed front-runner with more than $13 million in her war chest, unprecedented name recognition and a full Senate term under her belt,
Clinton cuts a unique figure, one she says will enable her to win.
"I'm in, in to win and that's what I intend to do," she said.
Of course, Clinton steps into the fray with plenty of negatives. She's regularly called one of the most divisive people in politics, but her team says they heard all of this before.
Clinton told Couric that regarding those who question her electability, "I would say, give me a chance.
"As a friend of mine said the other day, I am the most famous woman that nobody really knows. Because I've been caricaturized to some extent, and I want to let people make their own decisions," Clinton added. "And I think that I can do that as I have in here in our state."
Howard Wolfson, a senior adviser to Clinton, conceded that there were those who did not like her.
"There are Republicans that don't like her. At the end of the day there are a set of Republicans who won't vote for any Democrats," he told CBS News' The Early Show on Monday.
Wolfson pointed to a new Washington Post-ABC News poll showing Clinton is the favorite of 41 percent of Democrats, more than double the support of any of her rivals, to refute claims that she can't win.
"For people who wonder whether Senator Clinton can win, we say Senator Clinton is already winning in the polls," he said.
Asked how the Clinton campaign will deal with some of the scandals of her husband's presidency, Wolfson said, "I don't think voters care about those."
He said former President Bill Clinton "is her biggest supporter and always gives her advice. He campaigned for her in 2000, in 2006; everywhere he went he was a big success. We are looking forward to him on the campaign trail."
Sen. Clinton was scheduled to start a three-day series of Web chats with supporters Monday evening. She travels to Iowa, site of the first nominating caucuses to select delegates to the party's national convention, next weekend.
"As I said when I launched on Saturday, 'let the conversation begin' because I think through that conversation we'll be able to chart the best course for our country," Clinton told Couric.
Clinton and Obama are the most visible candidates in a Democratic field that includes the 2004 vice presidential nominee, John Edwards. Other candidates include Connecticut Sen. Chris Dodd, former Iowa Gov. Tom Vilsack and Ohio Rep. Dennis Kucinich.
Clinton told Couric she has "no doubt" Obama is "an extraordinarily talented person, and I am pleased we have such a talented field. I think we're going to have a great debate."