Why doesn't Kerry run again? This seems somewhat strange to me that he would decide to not run in 2008. And if immigration reform passes, Huckabee, who gave in state tuition to illegals in Arkansas, probably is not going to benefit. Tom Tancredo and Duncan Hunter would the beneficiaries of that, and later, Mitt Romney, who was very pleasing to the restrictionist wing of the party in 2008 and 2012. He would end up reeping the benefits of that. Huckabee had to do well with the religious right and with the economic populist right, and by and large, he was able to in 2008, but Republican electorates vote for the candidate who speaks on the issues in the forefront of their minds (the surge led to good support for McCain), and in this case, he wouldn't have it, unless he drastically changed his views on illegal immigration issues.I'll give this a try.
2004: Bush doesn't back down over the STELLAR WIND program, and this results in a mass resignation of FBI and DoJ officials led by Director Mueller; this is enough to get Kerry over the edge in New Mexico, Iowa and Ohio, giving him the victory in the EC but he still loses the popular vote.
2005-2006: President Kerry begins a pullout of Iraq, which begins to collapse into a civil war without the American presence. Republicans are able to retain and expand their majorities in both chambers of Congress in the Midterms. Hillary Clinton does better in her Senate campaign, and avoids going into debt as deeply as she did.
2007: Attempt at Immigration Reform passes in the Senate, led by a coalition of Democrats and establishment GOP figures like George Allen, but dies in the House. This provokes great anger in the Republican base going into 2008.
2008: Huckabee establishes himself as the Populist candidate in the Republican primary, winning Iowa (as per OTL) and then South Carolina after establishment front runners McCain and Allen got into a bruising fight over New Hampshire. Momentum is able to carry him from there to victory. On the Democratic side, HRC and Obama have a bruising primary that Clinton ultimately wins, thanks to getting the support of Kerry. As the fall campaign shapes up, Huckabee is able to take advantage over the split within the Democratic Party by selecting J.C. Watts as his running mate and hitting Clinton from her left on some economic issues; with the collapse of the economy and the matter of Iraq, however, the final outcome isn't ever really in doubt.
Huckabee for all of his gerontocratic tendencies did very well with young Republicans in 2008 and really connected well with young devout Christians active in the Christian music scene and the youth groups and all of that. He could speak to youth culture while also framing things in his outlook as a Baptist preacher.Again, I'm interested in exploring what a Huckabee victory in 2008 would look like as a social and cultural development as much as a political development.
I'd Obama's victory was was a very important moment for American society. It was obviously huge that American elected a black person as POTUS, but even more than that, Obama's victory was taken to signify the newfound clout of the "coalition of the ascendant." These were the young voters, educated voters, socially liberal voters, women voters, and voters of color who were considered the core of Obama's base. I'd also argue that Obama's victory played a huge role in energizing the various causes championed by these groups. Think of how much progress the LGBT movement has made in the ensuing years, especially with respect to gay marriage and the status of trans people. Think of how much more feminist society is today than it was at the beginning of the 2010s (seriously, something like the Weinstein effect would've been unthinkable this time ten years ago). Think of the genesis of the Black Lives Matter movement. Heck, think of all the media attention the various hipster subcultures got in the early 2000s.
Now, replace Barack Obama with a man whose coalition is almost the polar opposite - much older, much whiter, much more religious, much more rural. Even if, as @David T sughests, the election of Huckabee is taken as a fluke (which it almost certainly would be), such a change to the 2008 election would have a huge effect on the American culture. The Christian Right's influence would be far, far stronger, by virtue of counting the President of the United States among their number.