If you find yourself running late stuck in Tampa traffic, it is pretty straightforward coming into Tampa to get off of the highway and take an alternate route into the airport. Get off of I-4 before the I-75 split, at 22nd St in Ybor City. Go north on 22nd for 3 blocks and take a left (westbound) on 17th Street. This is a residential street. Stay on 17th westbound, it will merge with Columbus Avenue. Columbus Avenue eventually changes name to Boy Scout Road -- Boy Scout Road is actually the airport service road that runs parallel north of I-275; it will take you right in. (Take a look at Google maps and you'll see how simple this detour is, ~ 6 miles on surface streets. Columbus does go as far east at 22nd St., but that end of Columbus is one-way, so you can't turn directly onto it at first.)
The bulk of the ugly highway traffic in that part of Tampa is at the I-75/I-275 split; if it's backed up, just bail and avoid it.