(CNN) -- After Mitt Romney swept the five Republican primaries being contested Tuesday, 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.
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 LaBolt said, "The fact is a better title for Gov. Romney's speech tonight, [rather] 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 Obama already has clinched the Democratic nomination, as expected.
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 have 23 events here in North Carolina this week. We are going to be at 23 events in North Carolina this week."
He also vowed, "We are going to go to Tampa (site of the Republican National Convention in August) to fight for an American energy independence plan so no American president will ever again bow to a Saudi king." But he didn't say that he would fight on for the nomination as he has in previous speeches but instead said he wanted "to be sure conservatism is fully represented in Tampa."
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.
Santorum has yet to endorse Romney and declined to do so despite repeated prodding from Morgan on "Piers Morgan Tonight."
The former candidate said that he hoped to meet with Romney "in the next week or two" and two senior advisers to Santorum's campaign told CNN that the meeting with Romney is tentatively scheduled for May 4, and the agenda would likely include the possibility of an endorsement and the role of conservative issues on Romney's platform.
Romney's campaign has already been working behind the scenes to build up its general election organization, engaged in a "rapid build-out" and concentrating on hiring more staff at its Boston headquarters and in some key states, a Romney adviser said.
Part of the transition to general election mode would include expanding media access to Romney's fundraisers, the adviser said.
As the campaign moves forward, the adviser said Romney will continue making more "direct engagement" with Obama, and cited "some of the exchanges we've had over the past seven to 10 days" with the president as proof the general election has begun.
A Republican strategist said the contest had already turned a corner before Tuesday.
"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," said CNN contributor Alex Castellanos. "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 presidential run but who is not taking sides this cycle.
With the nominating fight in his rearview mirror, Romney is free to focus more on building up his war chest for the general election. He plans a series of fundraising events Wednesday and Thursday in New York and New Jersey.
"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.
Without naming Romney, Obama sought to distinguish his background from that of the multimillionaire businessman and former Massachusetts governor.
"This is something Michelle and I know about firsthand," Obama said of student debt, pausing amid cheers and laughter from the energetic crowd. "I just want everybody here to understand. ... I didn't just read about this. I didn't just get some talking points about this. I didn't get some policy briefing on this. Michelle and I -- we have been in your shoes. Like I said, we didn't come from wealthy families."
Obama repeated that theme at the University of Colorado later Tuesday, telling a crowd there, "Michelle and I graduated with a mountain of debt."
He also taped an appearance on "Late Night With Jimmy Fallon," a show popular with college-aged viewers, at UNC, in which he spoke more on the issue with the host.
Obama ends the tour on Wednesday at the University of Iowa.
All three universities are in states that Obama narrowly won in the 2008 election, which are considered battleground states again in 2012.
Five years ago, rates for the popular student loan program were lowered to 3.4% from 6.8%. Without an extension, the lowered rates are set to expire on July 1 and return to 6.8%.
In a rare show of agreement with Obama, Romney said Monday he supports extending the lowered loan rates for low- and middle-income undergraduates.
"With the number of college graduates who can't find work or who can only find work well beneath their skill level, I fully support the effort to extend the low interest rate on student loans," Romney said before a campaign event in Astor, Pennsylvania.
Last year, when asked about the rising cost of higher education, Romney suggested that market forces would lead some colleges to lower the price of receiving an education to compete in attracting cost-conscious students.
Senate Republican leader Mitch McConnell, R-Kentucky, indicated Tuesday that an agreement would be worked out in view of the support for extending the lower loan rate by Obama and Romney.
Romney needs to overcome a big Obama advantage among young voters. In 2008, voters ages 18 to 29 supported Obama over Republican nominee Sen. John McCain by 66% to 32%, according to CNN exit polling.
Obama has maintained his lead among the group, according to the latest CNN/ORC International Poll, with 64% support to Romney's 32%.
Rep. Aaron Schock of Illinois, a Romney surrogate who is the youngest member of Congress, argued Tuesday that Obama's rhetoric has not translated into a better culture for young voters.
"The reality is there's not been opportunity for young people as they've graduated from college," Schock said on a conference call with reporters organized by the Romney campaign. "Half of the young people who graduated last year are still unemployed or underemployed. Nearly the same percent still live with their parents."
CNN's Kevin Bohn, Tom Cohen, John Helton, Ashley Killough, Shawna Shepherd, Paul Steinhauser and Rachel Streitfeld contributed to this report.