US Senator Warren speaks at the Center for American Progress' 2014 Policy Conference in Washington Thomson Reuters MANCHESTER, N.H. (Reuters) - The scene in the New Hampshire office is one common to any nascent U.S. presidential campaign in the state that holds the country's first primary contest: Young staffers peck away at laptops and unpack boxes of signs with their candidate's name.

But the Democrat they are working for, U.S. Senator Elizabeth Warren of Massachusetts, adamantly denies plans to seek the presidency.

Backed with $1.25 million from liberal advocacy groups MoveOn.org and Democracy for America, the "Run Warren Run" group has opened offices in New Hampshire and Iowa, hoping she will jump in and contending Warren's message of populist economics could propel her into the White House in 2016.

This core of supporters believe Warren could beat presumed party frontrunner and former secretary of state Hillary Clinton, who is expected to formally launch her campaign in coming months and who holds a huge lead over other possible Democratic candidates in opinion polls.

Even outside the Warren camp, some other Democrats says a challenger to Clinton could help the party's chances by ensuring she entered the general election campaign well-prepared, and by focusing attention on economic issues that matter to middle and lower income Americans, such as promoting a higher minimum wage and student loan reform.

MoveOn.org, which wants to see Warren in the race and her ideas heard, is a political powerhouse with a grass-roots organization that helped elect and re-elect President Barack Obama, including his long and hard-fought battle with Clinton for the Democratic nomination in 2008. Democracy for America has its own strong pedigree, dating back to Vermont Democrat Howard Dean's 2004 presidential run.

"We believe that she would be the strongest candidate in the general election," said Kurt Ehrenberg, a veteran political operative who is heading up the Run Warren Run operation in New Hampshire. "Our job is not only to convince Senator Warren to get into the race, it's to focus the race on these issues."

At Run Warren Run's Manchester office, Ehrenberg and three young staffers were busy organizing volunteers to hit the streets of four New Hampshire cities this weekend to spread the Warren message.

"The plan is for us to build a campaign, to show Senator Warren that if she does decide to get into the race, there is a ready-made structure here in New Hampshire and Iowa," Ehrenberg said. "We're going to build an organization that is ready to go it she decides to run for president."

Despite 300,000 signatures on a petition urging Warren, 65, to run, that is still a big if. "As Senator Warren has said many times, she is not running for president and doesn't support these draft campaigns," Warren's spokeswoman, Lacey Rose, said in an e-mail.

Senator Elizabeth Warren and Former US Secretary of State Hillary Clinton. Gary Cameron & Brendan McDermid/Reuters/Amanda Macias/Business Insider

SHAKING UP THE PRIMARY RACE

Warren's progressive views would make her chances of defeating a moderate Republican for the White House unlikely, but her appeal to the liberal flank of the Democratic Party is rooted in dogged opposition to perceived Wall Street excesses.

She grew up on what she has called the "ragged edge of the middle class," and as a Harvard law professor was among the first to warn of the looming sub-prime mortgage crisis that triggered the financial crisis of 2008.

She was a key architect of the Consumer Financial Protection Bureau set up after the crisis and since winning a Senate seat in 2012 has been a strong voice on financial issues, including helping block a former Lazard banker from winning a top job at the Treasury Department.

Publicly, Democratic strategists in Washington back Clinton's White House bid and say it is unlikely another viable candidate will emerge unless she decides not to run. Privately, many of the same people say they would like to see a more progressive candidate enter the race, if only to push the conversation to the left during the primary contests.

Clinton's potentially smooth path to the nomination stands in sharp contrast to the crowded Republican field, where about a dozen candidates are at various stages of exploring runs.

The Iowa caucuses and New Hampshire primary will take place early next year, kicking off a series of primary contests that culminate in each party picking its candidate to run in the November election.

"Candidates don't like primaries, but primaries traditionally will make candidates stronger for the general election," said Neil Levesque, executive director of the New Hampshire Institute of Politics. "While all the Republicans are fighting amongst themselves, they're all having a chance to get on TV for a year. When there's only one candidate, it's more difficult to do that."

Clinton has a commanding lead among Democrats who are likely to vote in the New Hampshire primary, with 58 percent saying she would be their choice if the primary was held today, according to a University of New Hampshire/WMUR poll released last week.

Warren ran second, with the support of 14 percent of 297 likely voters polled Jan. 22-Feb. 3, leading third-placed Vice President Joe Biden. The poll had a 5.7 percent margin of error.

But a poll commissioned by Run Warren Run found that 98 percent of likely Democratic voters in New Hampshire and Iowa wanted a competitive race. Some 79 percent of 800 respondents polled Jan. 30 through Feb. 5 said they would like to see Warren run, though that did not mean they would vote for her.

(Additional reporting by Amanda Becker in Washington; Editing by Frances Kerry)