The former Massachusetts governor, who on Saturday , gave an exclusive interview to Face The Nation Friday night.
"I believe in the principles of my party," Romney told Bob Schieffer. "And I believe that the only way that we're going to take the White House is not by acting like Hillary Clinton, but by holding true to the principles of our party, which is a coalition of social, economic and foreign policy conservatives."
Others in the Republican field, however, have questioned Romney's positions on abortion rights, immigration and gun control. They accuse Romney of running as a conservative in this election but taking more liberal stances in his campaigns for governor and for the U.S. Senate.
"It's not just the abortion issue, although he certainly was passionate in his advocacy for being pro-choice," Sen. John McCain, R-Arizona, said last week on Face The Nation. "I mean, look at literally every major issue. Whether it be immigration reform or taxes or immigration or any other issue, there has been changes in his position."
"Obviously, my position did change with regards to life," Romney said in response. "But on other issues, my positions have been very consistent with my principles and my views."
He pointed to what he saw as the evolving positions McCain has taken on abortion rights and immigration.
Romney said, "I'd note that as I look at the other candidates who are running for president, over time they look at specific areas and say, 'gosh, I was wrong on this. That needs to be adjusted'."
But Romney's critics point his politics in Massachusetts as evidence that he is not as true to the GOP as he is trying to make himself out to be. In 1992, Romney, then registered as an Independent, voted for Democrat Paul Tsongas in the presidential primary. He said Sunday that his vote was a political move meant to undercut the stronger Democrat.
"When there's no contest of significance on the Republican side, when you register as an Independent, you can vote in the Democratic primary and vote against Bill Clinton," Romney said. "I used to vote against Ted Kennedy, all right? So that's something that you get to do."
Romney's critics also look to his unsuccessful 1994 Senate race against Kennedy for more proof that Romney has not always been faithful to the party.
Schieffer pointed out that during that race Romney turned away from the Republican patriarch President Ronald Reagan, saying, "I'm not trying to return to Reagan-Bush."
"There's no question that the older I get, the smarter Ronald Reagan gets," Romney said. "When I was running in '94, I wasn't trying to return to Reagan-Bush, because that was characterized as a very different posture than what I was running for. I was talking about my own vision. I wasn't trying to be a copy of anybody else."
Romney's promise in that 1994 campaign to be a stronger advocate for gay rights than Kennedy has also rankled social conservatives who want a constitutional amendment banning same-sex marriage.
"For some voters, it might be enough to simply match my opponent's record in this area," he wrote in a 1994 letter to the Log Cabin Club of Massachusetts. "But I believe we can and must do better. If we are to achieve the goals we share, we must make equality for gays and lesbians a mainstream concern. My opponent cannot do this. I can and will."
"I also told gays in 1994 that I opposed gay marriage and civil union, because gay rights didn't include - at that time, people weren't talking about gay marriage and civil unions - so I've always opposed gay marriage," Romney told Schieffer. "But at the same time, I don't discriminate against people. I don't discriminate against gay people."
Romney said he has been a "strong advocate" for an amendment that defines marriage as a relationship between a man and a woman.
Religion is another issue that could be an obstacle in Romney's run for the White House. Evangelical Christians, like those who gathered at this weekend's Values Voters Summit, are a major force in the Republican Party, and Romney is a Mormon.
"I'm not going to try and distance myself in any way, shape or form from my faith. It was the faith of my fathers, of my sons, a long tradition in my family," he said. "I'm, as I say, true blue through and through. And so I accept the teachings of our church, and I do my best to live by those teachings."
Romney did not answer specific questions about Mormonism, saying the church would be better at answering them, but he pointed out its similarities with Christianity and Judaism.
"What I can tell you is that the values of my faith are founded on Judeo-Christian principles, and the same kind of philosophy that's associated with other Christian faiths and the Jewish faith and others is very much consistent with ours," Romney said.
Echoing John F. Kennedy, who in 1960 explained how his Catholic faith would impact his presidency, Romney said that his allegiance was to the Unite States, rather than to his church.
"If I'm president of the United States and put my hand on the Bible, I do what the Constitution tells me, what the rule of law tells me," Romney said. "I certainly don't do what leader of my church or any other tells me to do."