"It doesn't need a turnaround," Romney told CBS' "60 Minutes" in recorded remarks that aired Sunday night side by side with separately recorded remarks by Obama.
"We've got a campaign which is tied [in voter polls] with an incumbent president to the United States," Romney said.
A United Press International Poll released Saturday gives Obama a 4-percentage-point lead over Romney, with a 3.5-percentage-point margin of error.
Other national polls give Obama an average 3.7-point lead, in some cases within error margins, polling data aggregated by RealClearPolitics indicated.
Romney was asked about a video at a May fundraiser made public last week in which he said 47 percent of the American people paid no income taxes, were dependent on government and would never vote for him.
Republican critics have called for a campaign shake-up in the wake of the furor over the remarks and other issues.
"That's not the campaign. That was me, right?" Romney said of the contentious remarks.
"I've got a very effective campaign. It's doing a very good job," Romney said. "But not everything I say is elegant. And I want to make it very clear -- I want to help 100 percent of the American people."
On income taxes, Romney said he would lower all rates by 20 percent and offset that by eliminating deductions and exemptions, "particularly for people at the high end."
"There should be no tax reduction for high-income people," he said.
He said he thought it made sense for people like him who make their money from investments to pay a lower income-tax rate than those who make money from a salary or wages.
"It is a low rate. And one of the reasons why the capital-gains tax rate is lower is because capital has already been taxed once at the corporate level, as high as 35 percent," Romney said.
When asked if he thought a lower tax rate was fair, he said: "Yeah, I think it's the right way to encourage economic growth, to get people to invest, to start businesses, to put people to work."
Corporate tax rates also should fall and offset that by getting rid of "some of the loopholes, deductions, special deals, such that we're able to pay for the reduction."
"I don't want a reduction in revenue coming into the government," he said.
He declined to say what deductions, exemptions, loopholes and special deals he would eliminate for individuals or corporations.
Romney said he would save $100 billion by cutting out the healthcare reform enacted under Obama, another $100 billion from Medicaid and yet another $100 billion by turning major federal programs over to the states.
He proposes means-testing for Social Security and Medicare benefits for future retirees, so richer retirees would get less benefits than poorer ones. He also distanced himself from running mate Paul Ryan's plans to cut $716 billion in payments to Medicare.
"Yeah, he was going to use that money to reduce the budget deficit. I'm putting it back into Medicare and I'm the guy running for president, not him," Romney said.
Obama told "60 Minutes" Romney's contention that he is crushing economic freedom with taxes, regulations and high-cost healthcare is "a lot of rhetoric, but there aren't a lot of facts supporting it."
"I've cut taxes for middle class families by an average of $3,600 per typical family. When it comes to regulations, I've issued fewer regulations than my predecessor, George Bush, did during that same period in office," Obama said.
"Now, I don't make any apologies for putting in place regulations to make sure banks don't make reckless bets and then expect taxpayers to bail them out. I don't make any apologies for regulating insurance companies, so that they can't drop a family's coverage, just when somebody in their family needs it most.
"And, you know, the problem that Gov. Romney has is that he seems to only have one note: tax cuts for the wealthy and rolling back regulations as a recipe for success. Well, we tried that vigorously between 2001 and 2008. And it didn't work out so well."
Obama told the program his biggest regret was failing in a central promise of his 2008 campaign -- to change the tone of Washington.
"I'm the first one to confess that the spirit that I brought to Washington, that I wanted to see instituted, where we weren't constantly in a political slugfest but were focused more on problem-solving that, you know, I haven't fully accomplished that. Haven't even come close in some cases," he said.
When asked if he bore any responsibility for that, he said: "Oh, I think that, you know, as president I bear responsibility for everything to some degree."
He said that despite two years of political gridlock between the White House and Republican lawmakers, he hoped the relationship would become more cooperative after the November election.
"I'm hoping that after the smoke clears and the election season's over that that spirit of cooperation comes more to the fore," he said.
Obama and Romney both said their workdays typically end about 10 p.m., but they described their late-night routines as being different.
Obama said that after his wife, Michelle, and daughters, Malia and Sasha, went to sleep, "I've got those hours between 10 and 1 in the morning, let's say, where not only do I do some work, but I do some reading, I do some writing.
"There are times where I sit out on the Truman Balcony [overlooking the White House South Lawn] and it's as good of a view as you get, with the Washington Monument and the Jefferson Memorial set back behind that," Obama said. "And so those are moments of reflection that, you know, help gird you for the next challenge and the next day."
Romney said he typically ends his day with a conversation with his wife, Ann, and then reads and plans what he wants to accomplish the next day.
He added: "I pray. Prayer is a time to connect with the divine, but also time, I'm sure, to concentrate one's thoughts, to meditate, and to imagine what might be."
He said he prayed every night before going to bed.
When asked what he prayed for, Romney said: "That's between me and God. But mostly wisdom and understanding. I seek to understand things that I don't understand."