President Barack Obama said during a Tuesday press conference that he doubts Donald Trump will succeed him in the White House because 'I have a lot of faith in the American people, and I think they recognize that being president is a serious job.'

Trump fired back hours later in coastal South Carolina, telling an overflow crowd that Obama 'has done such a bad job! He has set us back so far. And for him to say that actually is a great compliment.'

Obama told reporters in California that he would 'leave it to you to speculate how this whole race is gonna go. I continue to believe that Mr. Trump will not be president.'

'It's not hosting a talk show, or a reality show, it's not promotion, it's not marketing – it's hard,' he said of the U.S. presidency. 'And a lot of people count on us getting it right.'

'And it's not a matter of pandering and doing whatever will get you in the news on a given day

Obama assessed both the Democratic and Republican ends of the race in response to questions posed to him at a California press conference at the conclusion of the first-ever Association of Southeast Asian Nations conference on U.S. soil.

Trump was on stage in a Beaufort, South Carolina high school auditorium fielding questions from Van Hipp, a former chairman of the state GOP.

South Carolina's statewide Republican presidential primary election is set for Saturday, and the billionaire first-time candidate is leading the field by a mile. 

'He has done such a lousy job as president,' Trump said, to roaring applause.

'You look at our budgets, you look at our spending. We can't beat ISIS. Obamacare is terrible – we're going to terminate it. We're going to absolutely terminate and replace it.'

'I mean, you look at everything,' Trump said. 'Our borders are like Swiss cheese.'

He said during his ride to the high school a television network had called him for a reaction to Obama's harsh words. As he re-told the story, he put his response the way he would if he were talking to the man whose job he wants.

'You're lucky I didn't run last time when Romney ran,' he said, 'because you would have been a one-term president.' 

Democrats have been fighting over who is the rightful heir to Obama's legacy in the White House - the president's former secretary of state Hillary Clinton or progressive champion and U.S. Senator Bernie Sanders. 

Clinton accused Sanders of being disloyal to Obama last week after he said during an MSNBC interview that Obama had tried but failed to close the 'presidential leadership' gap.

Obama said he doesn't understand why other Republicans running are not being scrutinized as heavily for their proposals as Trump given that there are other running on'anti-Muslim' and 'anti-immigrant' platforms. 

'I don't think it's restricted by the way to Mr. Trump,' he said. 'I find it interesting that everybody's focused on Trump, primarily because he says in more interesting ways.'

But it's what the other candidates stand for, as well, Obama said.

'So he may up the ante in anti-Muslim sentiment, but if you look at what the other Republican candidates have said, that's pretty troubling, too.'

Obama pinpointed U.S. Senator Marco Rubio of Florida, a sponsor of the failed Gang of 8 Senate bill to reform the immigration system. 

'You've got a candidate who sponsored a bill that I supported...and he's running away from it as fast as he can,' Obama said, referring to Rubio's position now that comprehensive reform is a no-go until the border is secure.

Of all the candidates, Obama said, 'They're all denying climate change.'

'I think that's troubling to the international community,' the U.S. leader said