Is it possible Bush 43 would even tried to seek a 3rd term in 2008 ?
In otl 2008, no. But think - if he was starting his second term with re-election in mind, he might have been more careful with policy decisions. Maybe he visits following Katrina, sack Rumsfeld immediately, earlier surge in Iraq followed by the beginning of a drawdown of forces - maybe even all in time for the midterms. Hell, maybe even do away with talk about bombing Iran.
With re-election in mind, many decisions made by both President and Congress in second terms of Presidents would be much, much different - Reagan and Iran-Contra, Clinton and impeachment, Bush and...everything. And potentially we'd be looking at a very different Obama term, and speculating about a potential primary challenge from Clinton. Why did she step down as SecState following his first term? Is she trying to distance herself from the Administration in preparation to run in 2016 - whether Obama runs or not?