(CNN) -- Sen. John McCain said Wednesday that he will bring the Republican Party together to win the presidency.
"We will unite the party behind our conservative principles and move forward and win the general election in November," the Arizona senator said the day after significantly padding his lead over rivals Mitt Romney and Mike Huckabee.
Standing in front of his "Straight Talk Express" bus, flanked by the man he has called his "favorite Democrat," independent Sen. Joe Lieberman of Connecticut, and Sen. Lindsey Graham, R-South Carolina, McCain said he was "pleased at the depth and breadth of our victory last night."
Supporters like Lieberman and Graham, he said, "gave us a broad base of support from all parts of this party."
McCain said he has canceled a planned trip abroad this weekend in order to "wrap this up as quickly as possible." Watch what McCain says about his relationship with conservatives »
McCain took the lion's share of Republican delegates on Super Tuesday, but still had only about 52 percent of the number needed to secure his party's nomination. Watch why analyst says Super Tuesday not decisive »
On the Democratic side, Sen. Hillary Clinton comes away with about 41 percent of the delegates needed for the nomination while Sen. Barack Obama sits at 36 percent.
Fewer than 50 votes separate Obama and Clinton in New Mexico, with 98 percent of Tuesday's vote counted.
McCain said he is not worried about concern among "very conservative" Republicans that he is not conservative enough for their tastes.
"With conservative voters, which are the majority of Republicans, we did extremely well," he said.
Comparing his home state with that of his more conservative rival, he said, "We won by a much larger margin in Arizona than Gov. Romney did in Massachusetts."
"Is there a lot of work to unite the entire party?" he asked rhetorically. "Sure. After the campaigns are over, you've always got the task of uniting the party behind the nominee."
But he expressed confidence he can do just that.
"Our message will be we all share common conservative principles," he said. "Fundamental conservative political philosophy, which has been my record."
Now the focus of the presidential races is on primaries in Virginia, Maryland and the District of Columbia next Tuesday.
The candidates hope to gain momentum for those with victories in the Louisiana primaries and Washington state caucuses on Saturday. Watch why the races will go on »
Both the Obama and Clinton campaigns believe Obama has an edge in those races. Clinton will focus on March 4 primaries in Texas and especially Ohio, said the Web site Politico's executive editor Jim VandeHei.
"There are a lot of working-class whites [in Ohio] and she feels she does extraordinarily well with that demographic," VandeHei said on CNN's "American Morning."
Further along, the Clinton camp sees Pennsylvania on April 22 as a state where the demographics work in her favor.
"I look forward to continuing our campaign and our debates about how to leave this country better off for the next generation, because that is the work of my life," Clinton said Tuesday night.
Although Clinton took the majority of delegates in large states like California, New York and New Jersey on Tuesday, Obama won more states overall, 13 to Clinton's eight. Full February 5 results
Obama said Wednesday he scored a "big victory" on Tuesday and that he was overcoming Clinton's "political machine" that made her the front-runner in every race.
"This campaign is gaining momentum by the day," he said at a Chicago news conference, repeating his mantra that he is the Democrat who can bring about change.
Howard Wolfson, Clinton's communications director, called for one debate a week between the two Democrats leading up to the March 4 primaries in Ohio and Texas.
"We won the votes of people who decided on the last day. We did that in large measure ... because of a very strong debate performance," Wolfson said.
Democratic Party Chairman Howard Dean expressed satisfaction Wednesday with the primaries and what the Super Tuesday results mean for his party.
"I think it's good that we go deep in the nominating process," Dean said. "I want our candidates to be exposed in all of the states -- in places like Pennsylvania and Washington D.C., and Virginia, Maryland, Wisconsin. Good for the Democratic Party, good for the country to see candidates up close," Dean said on CNN's "American Morning."
McCain is the clear front-runner among the Republicans. He's won more than double the number of delegates than Romney, the former Massachusetts governor, and more than three times those earned by former Arkansas Gov. Huckabee. More about delegates
Huckabee, buoyed by victories Tuesday in Arkansas, West Virginia, Georgia, Tennessee and Alabama, pledged Wednesday to stay in the race until the end.
"It may be that none of us have enough [delegates] to win the whole thing until we get to the convention," he said. "If I don't stay in the race, I can't win."
Romney on Tuesday won Massachusetts and Utah and came out on top in caucuses in Alaska, Montana, North Dakota and Minnesota. It was enough to keep him plugging.
"We're going to battle, go all the way to the convention, win this thing, and get to the White House," Romney said Tuesday night.
But top Romney advisers acknowledged that it will be difficult to overcome McCain's lead.
"It is tough to saddle up this a.m.," one Romney adviser told CNN. E-mail to a friend
All About Barack Obama • Hillary Clinton • John McCain • Mitt Romney • Mike Huckabee