"He would not have his contract renewed," Graham said on CBS' "Face the Nation."
However, former presidential senior adviser David Axelrod said the 2012 election "isn't just going to be about the president. It's going to be about what direction we want to take as a country."
The two traded views about Obama's chances of winning re-election just two days after the first-ever downgraded credit rating following a bitter fight to tie lowering the federal deficits to raising the debt limit.
"We have to do much, much better," Axelrod said, noting Obama has proposed extending the payroll tax cut and unemployment insurance, enacting an infrastructure bank to preserve construction jobs, passing trade treaties to expand exports and reforming patent and tax laws.
"There are things we can do to move this country forward," he said. "What we need is cooperation and action on the part of the Congress."
If Washington acts on those areas as soon as Congress returns from its August recess, "that would have a positive impact on the economy," Axelrod said. "The question is whether we have the will to do it and whether we can lay the politics aside and work together, Republicans and Democrats, to do it."
Obama has had three years to move the economy "and he's failing," Graham said.
"He's had a chance," Graham said, later saying, "This president has failed to lead and in any other private sector enterprise he would be fired. If he was asking to be re-upped to run a football team, they wouldn't hire him. If he was trying to be a CEO for a second contract, he wouldn't be hired."
The Republican Party has a chance, but "we've got to be for things," Graham said, such as a balanced budget amendment that would require both parties "to do what we should have done a long time ago."
Graham said he also was for adjusting entitlement programs and for closing the tax deduction loopholes to bring money back into the U.S. Treasury so the government could pay down its debt.
"So this president hasn't led. And the tale of the tape is in," Graham said. "Statistically this has been a lousy presidency only getting worse."