He also refuted claims by his opponent, former Massachusetts governor Mitt Romney, that the Arizona Senator was not a true conservative.
"First of all, if you examine my record, it's more conservative than Governor Romney's is," he told host Bob Schieffer. "I went to Iowa and told them that I was against subsidies for ethanol. He was for them. I went to Michigan and said the old automobile jobs aren't coming back; new ones are, but old ones aren't. He wants to give them $20 billion, to Detroit, over four years. We went to South Carolina - same kind of deal. So look, I am proud of my conservative record, and I will run on it.
"We carried Florida in a Republican-only primary," he said. "We got very large percentage of the 'conservative' vote. And I'm confident that once they examine my record and as we unite against a common opponent, we'll do fine with that."
McCain said that, if elected president, he would veto any attempt to raise taxes. "I think if we're going to be in some shaky times - and by the way, I believe the fundamentals of America's economy [are] still strong - then the worst thing you can do is increase taxes at that time."
He also sided with President Bush in maintaining tax breaks for upper income Americans and corporations. "I think everybody needs a tax cut," he said.
Later, Democratic presidential candidate Sen. Barack Obama of Illinois said his campaign was attracting not only Democrats but also independents and disenchanted Republicans - and could do so better than Sen. Hillary Clinton.
When asked about the chances that Clinton would attract more negative attacks from the GOP, Obama acknowledged "There is some history there, not all of Senator Clinton's making, but I don't think there's any doubt that the Republicans consider her a polarizing figure. Now, keep in mind, I don't expect, should I become the Democratic nominee, that I'm going to be immune from some of the attack that I think the Republican spin machine is so accustomed to.
"But what we have found - this is true in Illinois, when I was running for the United States Senate, I think it's going to be true nationally - is that the tone that I take, the ability to disagree without being disagreeable, the willingness to listen to Republicans about some of their ideas, even though I may not agree with all of them - I think that creates a different climate. And I think that we can attract independents and Republicans in a way that Senator Clinton cannot."
"I was in Idaho yesterday and we were up in Boise. We had 13,000 people come out to a rally. Keep in mind that four years ago, only 5,000 people participated in the Democratic caucus. And I think that's one of the untold stories of this campaign, is the enormous turnout that we've been seeing in the first four early states."
He disputed talk of a "brown/black divide" between Hispanic and African American voters, given how Clinton attracted more of the Hispanic vote in Nevada and elsewhere.
"There's no doubt that Senator Clinton is still more familiar with [the Hispanic community] than they are with me. But I think that that is changing. And I think we're making enormous progress.
"In Illinois, when I ran for the United States Senate, I got 75 percent of the Hispanic vote. In Iowa, where we had time to campaign and Hispanic voters knew my track record of working on issues that help with the education of Hispanic kids, and have a comprehensive immigration strategy that will deal with the problem in a way that isn't just having it used as a political football, we actually won in Hispanic precincts. So my challenge has always been to make sure that the Hispanic voters know who I am."
Finally, in light of the positive audience response during the most recent debate when it was suggested that both candidates be on the same ticket in November, Obama said it was "presumptuous" to consider that either he or Clinton would accept a vice presidential slot if the other won the nomination.
"I think she is running actively for the presidency, as I am. But I think that there's no doubt that Democrats are eager to unify against the Republicans."