Why is Jeb Bush sharing the stage with President Obama?

The scene on stage Friday at a Miami public high school will be eye-catching: the Republican former governor of Florida, Jeb Bush, alongside President Obama.

Education Secretary Arne Duncan invited former Governor Bush to appear with the president at an education event in Florida, and Bush in turn recommended the venue – Miami Central High School, which has made strides in turning itself around.

It’s obvious why Mr. Obama would want Bush there. He is a Republican star, albeit one who can’t run for president just yet, given lingering Bush fatigue. The presence of Jeb Bush, whose older brother George W. Bush also emphasized education during his presidency, puts a bipartisan seal of approval on Obama’s own education efforts.

But why is this a good move for Jeb Bush? He has made clear that he’s not running for office in 2012 (either president or Senate), but don’t rule out a presidential run in 2016. One of his big issues is education. During his two terms in Tallahassee, Bush fashioned himself as the “education governor,” then started the Foundation for Excellence in Education after leaving office in 2007. Its goals sound a lot like Obama’s: high expectations, data-driven accountability for teachers, outcome-based funding, helping the nation compete globally.

“It won’t hurt him nationally, because education is one of those issues that you do see a lot of cohesiveness on – with the exception of how to pay for it,” says Susan MacManus, a political scientist at the University of South Florida in Tampa.

So on Friday, don’t expect budget talk out of Bush when he’s up there with Obama, or references to the legislative standoff in Wisconsin over public unions. The Bushes are nothing if not well-mannered. Still, you have to wonder how the still-forming field of potential Republican presidential challengers will react when one of the party’s leading lights makes nice with the “enemy” in an important swing state like Florida.

Perhaps it’s a sign that Bush thinks Obama will be hard to beat, and so he might as well take advantage of the spotlight when it’s offered. He’s not saying.

One thing is for sure: If Bush has any say in the matter, there won’t be a photo op of Obama giving him a big hug, a la former Republican Gov. Charlie Crist, whose embrace with Obama dealt a mortal blow to his Senate campaign.

“The picture I want to see is Obama chasing [Bush] around the stage trying to give him a bear hug,” says Cal Jillson, a political scientist at Southern Methodist University in Dallas.