"I don't want to, as I say, to get into a war of words," Cameron said. "What matters is dealing with the issue. And the issue is, the spill in the gulf, the need to cap the wells, the need to make the payments."
"I'm interested in not making this into a U.S.-UK issue. It shouldn't' be," he said. "It's in our interests in the long term that this company has a strength and stability to be able to make those payments, clear up the spill and continue as a strong and independent and loyal business."
Cameron will meet with Obama later today to discuss a variety of leadership issues, including the war in Afghanistan and economic strategies.
He told Sawyer that while the shared mission in Afghanistan has gotten back on track, he's disappointed that the "world looked the other way" after the Taliban was largely removed and attention turned to the war in Iraq.
"For too long, we weren't pursuing the right strategy. For too long, we didn't have all the pieces in place," he said. "I profoundly believe now, at least we have got the pieces in place."
He reiterated past statements that he'd like to see British troops make yet another attempt to teach the Afghans to take responsibility for their own security and then withdraw combat forces by 2015.
But one strategy Cameron and Obama don't share is how to pull their respective countries out of their economic struggles. Obama has leaned heavily on stimulus plans meant to create jobs and boost spending. But Cameron --who said he was pleasantly surprised at Obama's "frankness" when they first met -- has talked about a tax increase and budget cuts of 20 to 25 percent, slicing across a multitude of government programs, including defense.
"America is still a reserve currency. You guys can run a bigger deficit for longer than we can," Cameron said. "But, you know, this year, we are borrowing more than virtually any other country in the G20."
"It's necessary for Britain to tighten its belt and to prove that we can live within our means," he said. "I mean, I'm a conservative. I believe that, you know, if you borrow too much, you just build up debts for your children to pay off. You put pressure on interest rates. You put at risk your economy. That's the case in Britain. "
"Well, there'll be the usual family row about who does what," Cameron joked. "I mean, I'll try and be a good, hands-on dad. But Sam and I have talked about it and she said, 'You know, I expect you to be a bit less hands-on this time around.'"
But Cameron said he's promised his wife – and himself – that he'll make time for family vacations and special moments.
"You've got to make sure that you do find time for your family and your children," he said. "If you get frazzled and fried and exhausted and forget who you are, then you're going to be a rubbish dad. But you'll probably be a rubbish prime minister too."