MANCHESTER, N.H. (AP) — Republican presidential candidate Mitt Romney, savoring a convincing primary win in New Hampshire, declared a "historic" victory to his supporters Tuesday and immediately turned his sights on the man he would replace, President Barack Obama.

"Americans know that our future is brighter and better than these troubled times," a triumphant Romney told the crowd. Surrounded by his children and grandchildren, Romney focused almost entirely on the Democratic president he would face in the general election if he goes on to become the nominee.

"We know that the future of this country is better than 8 percent or 9 percent unemployment. It is better than $15 trillion in debt. It is better than the misguided policies and broken promises of the last three years — and the failed leadership of one man," Romney said.

But he also called the increasingly fractured Republican field "desperate" and said the attacks his rivals have leveled on his business record are similar to Democratic criticisms.

"In the last few days, we have seen some desperate Republicans join forces with (Obama)," Romney said, speaking at Southern New Hampshire University. "This is such a mistake for our party and for our nation."

Romney said the attacks represented "a resentment of success."

The win makes Romney the first Republican presidential candidate to win nominating contests in both Iowa and New Hampshire and makes him the man to beat in the race for the GOP nomination.

"Tonight we made history," Romney declared.

"One, two!" said one supporter, punching the air with his fists. "Two down!" shouted another.

"It's a statement of confidence," said Kent Lucken, a longtime Romney business confidante.

The win puts Romney in a strong position heading into South Carolina's primary on Jan. 21, and the Jan. 31 contest in Florida. While Romney plans a campaign stop in Columbia, S.C., on Wednesday, he'll first attend a major national fundraising meeting at his campaign's headquarters in Boston.

Romney's campaign flew in more than 150 of its top donors from across the country to celebrate the victory, and they filled the risers at his victory party. Billionaire Hewlett Packard CEO Meg Whitman was in attendance, as was all of Romney's top financial staff.

After nearly a month of intense campaigning in early states, the campaign will shift its focus back to fundraising ahead of the ad-intensive Florida contest, and, potentially, the expensive general election. The Romney campaign plans a major fundraiser in Palm Beach, Fla., on Thursday, and another high-dollar event in New York early next week.

Still, Romney is preparing for a potentially bruising primary in South Carolina, where allies of rival Newt Gingrich already are airing millions of dollars in ads attacking his record at Bain Capital.

"Tonight we celebrate," Romney told his supporters. "Tomorrow we go back to work."

Romney aides said they are anticipating a brutal 10-day campaign to win South Carolina, a state with a reputation for nasty, down-and-dirty politicking. Romney's chief goal will be making sure none of his rivals is able to consolidate support there and emerge as a convincing conservative alternative to the former Massachusetts governor.

Preventing that from happening could turn Florida into the defining contest and allow Romney to move quickly to seal the nomination.

Romney's aides acknowledge making that happen will require a more aggressive defense of Romney's time at Bain. Texas Gov. Rick Perry, already campaigning in the state, called venture capital firms like Bain vultures that feed on the carcasses of struggling companies.