CONCORD, New Hampshire -- Hillary Clinton made it official in New Hampshire on Monday, filing paperwork to run for president in the nation's first primary.

"It's a good omen," Clinton said of the perfect 60 degree fall weather, to a room packed with reporters and beaming surrogates. "Bright and sunny."

It was not the first time Clinton has filed presidential papers in New Hampshire at the State House in Concord. Besides her unsuccessful 2008 campaign, the former first lady filed on behalf of her husband Bill Clinton in 1991 and again in 1995 when he was running for re-election.

"This is the fourth time that I've done this," Clinton said with a pen in her hand. "December of '91. I signed papers on behalf of my husband. Far different scene. Very few people gave him much of a chance. New Hampshire was very kind to him."

"Far different scene" was right: more than 300 supporters of Hillary packed the halls of the New Hampshire State House chanting "Hillary, Hillary" throughout her visit.

Also different this time around: a strong showing of former Obama backers from the 2008 race now with Clinton. The show of force was a reminder that Clinton is doing her best to fight back against long-standing questions about her ability to generate grassroots excitement.

"There's a lot of enthusiasm, as I just witnessed walking the hallway here walking to come to the office of the secretary of state," Clinton told reporters. "I'm going to run my campaign. I'm going to run as hard as I can. I'm going to make the case for what I think the country needs and do my very best to earn as many votes as I possibly can."

In the 2016 Democratic race, it's been Bernie Sanders who has been drawing the largest crowds and attracting young people to the race. But one Clinton supporter, State Rep. Laura Pantelakos of Portsmouth, criticized Sanders, a longtime independent, for his lack of Democratic party chops.

"Bernie is not a Democrat," Pantelakos said. "He's an independent, and I want a Democrat in office."

Clinton reminded reporters that she is a "loyal Democrat," a statement she made again after she filed to hundreds of her supporters gathered outside the State House.

Terry Shumaker, a longtime Clinton supporter, said the candidate has "a lot of new supporters" this time around.

"People who supported President Obama, people who weren't old enough to vote, you see the hallways are lined with young people," Shumaker said. "And then some of the people that supported her in '08 and some early Bill Clinton supporters like me that go back to 1991....It's pretty exciting. She's working to earn every vote, one day at time, and she knows New Hampshire well."

Clinton appeared to be in a chipper mood, fielding a wide range of questions from the New Hampshire press corps well past the "one question left" warning from her press secretary.

"Compare the performances," Clinton responded with a grin when a reporter pointed out that Donald Trump's "Saturday Night Live" ratings were higher than when she appeared in a sketch on the show in October.

One question Clinton declined to answer, however, was about whether the scrutiny that Republican front runner Ben Carson has undergone over the last week is appropriate, as questions about aspects of Carson's personal biography have emerged.

CBS News Political Digital Journalist Hannah Fraser-Chanpong contributed to this story.