(CNN) -- Mitt Romney swept the five Republican primaries being contested Tuesday, and he turned from securing the Republican nomination and toward the general election against President Barack Obama.

The former Massachusetts governor was projected to win in Connecticut, Delaware, New York, Pennsylvania and Rhode Island while New York.

With a big lead in delegates and his nearest competitor out of the race, Romney told a cheering victory rally in New Hampshire, "A better America starts tonight."

"The last few years have been the best that Barack Obama can do, but it's not the best America can do," Romney said. "Tonight is the beginning of the end of the disappointments of the Obama years and it's the start of a new and better chapter that we will write together."

Speaking to CNN's Piers Morgan after Romney's speech, Obama 2012 press secretary Ben DeBolt said, "The fact is a better title for Gov. Romney's speech tonight, than 'A Better America,' should have been 'Back to the Future,' because he's proposing the same economic policies that got us into the economic crisis in the first place."

Far ahead of the field in the battle for delegates, Romney became the presumptive nominee April 10 after his closest rival, former U.S. Sen. Rick Santorum of Pennsylvania, suspended his campaign. Even though former House Speaker Newt Gingrich and U.S. Rep. Ron Paul of Texas continue their long-shot bids for the White House, the party appears to be consolidating around Romney.

According to a CNN estimate, Romney has 695 of the 1,144 delegates needed, with Santorum holding 273 delegates, Gingrich 141 and Paul 72. By CNN's count, the earliest Romney could reach the nomination threshold is late May, while

Gingrich told NBC on Monday that he would "reassess" his campaign depending on how he finishes in Delaware, a winner-take-all state in which he has campaigned for several weeks.

"I think we need to take a deep look at what we are doing," Gingrich told NBC. "We will be in North Carolina tomorrow night, and we will look and see what the results are."

Gingrich spokesman R.C. Hammond said Gingrich would in the coming days "assess whether or not there is a path forward," and a decision could come "in a few days."

But in a concession speech in North Carolina on Tuesday, Gingrich said, "We are going to go to Tampa to fight for an American energy independence plan so no American president will ever again bow to a Saudi king."

Paul told CNBC on Monday that he won't step aside, even if Romney soon clinches the nomination.

"If tomorrow, Romney had the absolute number, I would probably continue in a modified way to maximize the number of delegates to go to the convention," Paul said on "Squawk Box," adding that his supporters insist he stay in the running.

"What is remarkable is how much this race has changed, now that it has become a general election contest between Mitt Romney and President Obama," Republican strategist and CNN contributor Alex Castellanos said. "The pathetically small GOP contest has been left behind."

"It has been replaced by a much larger election about two dramatically different views about what kind of country we are going to be and whether fairness or growth is our biggest problem," added Castellanos, who was a top media adviser for Romney's 2008 nomination bid but who is not taking sides this cycle.

Romney planned a series of fundraising events Wednesday and Thursday in New York and New Jersey, signaling his shift to general election mode after the latest primaries.

"Each fundraising event is important as we go towards the general election. He has been having much success in fundraising," said Phil Rosen, a major Romney contributor and co-host for a New York event. "There are two pieces of the puzzle: extreme dissatisfaction with President Obama. Second part: giant appeal of Gov. Romney on all aspects of the presidency."

Obama, meanwhile, delivered a fiery speech to college students Tuesday on holding down federal student loan rates, taking up an issue important to young voters by saying he wants them to have a fair shot at a degree without taking on a mountain of debt.

At the University of North Carolina, Obama recounted how the student debt he and first lady Michelle Obama owed after getting married exceeded their first mortgage.