Jeb Bush recommends Obama give 'tip of the hat' to brother on foreign policy

"I would argue that in some ways that by reality kind of seeping into his life as the commander-in-chief that a lot of it's modeled after ... 43," Bush said in an interview with CBS's "This Morning" host Charlie Rose.

"A little tip of the hat might be a nice thing," Bush added.

Bush also argued that recognizing the positive influence of his predecessor would be politically helpful for Obama.

"It helps to, just a small acknowledgment that the guy that you replaced isn't the source of every problem and the excuse of why you're not being successful, I think would help him politically," he said.

Bush offered praise for the administration's role in tackling education reform, specifically the progress made by Education Secretary Arne Duncan.

"Any time an elected official in the world we're in today, that appears so dysfunctional, challenges a core constituency — not of their opponent, but of their own political base — I think we should pause and give them credit," he said.

The former Florida governor said Obama has taken on his political party to better education in the United States.

"I don't have to play the game of being 100,000 percent against President Obama," Bush said.

Bush, who is not running for office himself, took a contrarian view from his political party as well, sparring with the GOP presidential field on whether they would agree to a deal that offered $10 in spending cuts for every $1 of tax revenue.

During a Republican presidential debate last August, none of the candidates agreed to the hypothetical situation.

"I can appreciate why they are reluctant to say that, because commitments on spending are hard to implement, commitments on raising taxes immediately happen," he said.

He also criticized the GOP for an inability to communicate its platform on immigration.

"I think there needs to be a lot more intense efforts to recognize the demographics of the country are changing and our messaging — not our views, not our principals, but how we message our views — needs to change," he said.

During the interview, Bush again adamantly denied any interest in the vice presidency.

"I'm not going to do it. I'm not going to be asked and it's not going to happen," he said.

Although he told CBS that "under no circumstances" would he serve as Mitt Romney's running mate, Bush said he is "enthusiastically" supporting the presumptive Republican nominee.

Read more on The Hill's GOP12 blog for insight into Bush's political future and more on his continued rejections of the vice presidential slot.