Hillary Clinton campaign's target: everyday folks

Hillary Clinton is very deliberately going small in Iowa, her first stop since announcing in an online video Sunday that she's running for president again.

First, she'll do a roundtable with some community college students, and then she'll visit a local fruit business, reports CBS News correspondent Nancy Cordes.

Her campaign is trying to convey that she's not expecting a coronation -- that she plans to work for every vote -- which was clearly the idea behind her announcement video.

Clinton doesn't appear in her own announcement video until it's almost over.

"My daughter is about to start kindergarten," one person says.

"I'm getting married this summer to someone I really care about," says another.

She's preceded by a diverse group of Americans, sharing big and small plans for the future.

"My brother and I are starting a new business," one person says, in Spanish.

"We're just trying to teach our dog to quit eating the trash," says another.

Finally, Clinton says, "I'm getting ready to do something, too. I'm running for president!"

And thus ends years of speculation about whether the former first lady and secretary of state would make a second run for the White House.

"Everyday Americans need a champion, and I want to be that champion," she says in the video.

The video reflects a philosophy laid out in a Clinton campaign mission statement obtained by CBS News. "We are humble," it reads. "We take nothing for granted."

In fact, advisers say this campaign is likely to look less like her first White House bid and more like her run for a Senate seat from New York in 2000, when she went on a listening tour of the state and even sometimes spent the night in supporters' homes.

"I'm hitting the road to earn your vote because it's your time and I hope you will join me on this journey," Hillary says in the video.

Republicans shot back with some videos of their own.

Ted Cruz said, "Hillary Clinton represents the failed policies of the past."

Carly Fiorina says, "She doesn't have a track record of leadership or trustworthiness."

And Jeb Bush says, "We must do better than the Obama-Clinton foreign policy."

Kentucky Sen. Rand Paul has an ad that airs starting today in four early voting states, including Iowa.

In it, he asserts, "Hillary Clinton represents the worst of the Washington machine."

Clinton's campaign says she's going to spend the next six to eight weeks in what they call a ramp-up phase, hiring staff, connecting with volunteers, and doing more small events, and that she'll probably do her first real rally sometime in May.

Now that she's officially in the race, Clinton has stepped down from her role at the Clinton Foundation.