My understanding of the "longevity argument" (with regard to keeping Terrell Davis out of the Hall of Fame) is something like this: yes, yes, he was a great running back, 2000 yards, Super Bowl MVP and all that* but he just didn't play long enough to qualify for the Hall of Fame. I have trouble understanding why this argument even exists when there are players like Gale Sayers, Doak Walker, etc. who were admitted to the Hall of Fame despite shorter careers than Davis.
A quick statistical comparison of Gale Sayers vs. TD:
Gale Sayers: played in 68 games total
4, 956 rushing yards
1, 307 receiving yards
2,781 kick off return yards
391 punt return yards
for 9,435 total all purpose yards ( excluding the 111 career passing yards he managed on 4 completions of 18 attempts)
That's a remarkable amount of production for 68 games, to be sure. But it's not as much as TD managed in his (16 game longer) career.
Terrell Davis: played in 86 games total (including the playoffs) which is roughly 26.5% more than Sayers!
7,607 regular season rushing yards (which is more than 53% more than Sayers)
1,140 post season rushing yards (Sayers never played in the post season)
So, 8,747 rushing yards total (roughly 76.5% more than Sayers)
1,280 regular season receiving yards (actually about even with Sayers)
131 receiving yards in the playoffs
Obviously, TD never returned punts or kickoffs yet he still had more overall yards than Sayers who got to play in a dual role.
60 Regular Season TDs
I'm not going to attempt to make a full comparison of Gale Sayers and Terrell Davis for 2 reasons: 1) Sayers retired before I was born and I don't think you tube clips would provide me with a proper appreciation for what made him great 2) I just don't think a perceived difference between Sayers and Davis is the primary problem. (For one thing he retired in 1971 and didn't play much at all in his last 2 years. And the Bears were a losing team every year he played with them and I imagine it was more difficult to watch games for teams in other cities at the time.... so I doubt many voters watched him when he played. And I don't imagine them carefully studying film to make a painstaking comparison of Sayers vs. TD)
The only concrete difference I've ever heard mentioned is that Sayers was more explosive. Even if this was true. So what? Joe Montana wasn't excluded from the Hall, nor forced to wait more than a decade for induction because he was less athletic than John Elway. Terrell Davis was (quite obviously) a great back in his own right and had achievements that were arguably even more impressive than Gale Sayers. Davis also played 18 more games and had many playoff records (whereas Sayers never played in a single playoff game). There is no consistent principle by which you could justify admitting Sayers on the first ballot, but never admitting TD at all. (unless you count a liking to elect former Bears players and diss the Broncos as a "principle")
In law "the use of precedent provides predictably, stability, fairness and efficiency in the law"  Can you imagine the choas, outrage and unrest that would ensue if binding precedent were observed in some cases with certain litigants and/or defendants and completely disregarded with others who were from a group that feels they have been discriminated against? Obviously the Hall of Fame committee members are never going to be held quite as accountable as a judge in a court (and precedent is a more complex concept than what I'm touching on here). But I do think that when individual voters seem to be making up their own criteria based (apparently) on their own whims, it greatly diminishes the perception of legitimacy and impartiality and calls into question their commitment to principle.
My impression from talking to random, ordinary fans who advocate some version of the longevity argument is that their main reason for taking this position is that they feel there is a back log of worthy candidates so it wouldn't be fair to admit someone with a relatively short career.
When I hear this type of argument, I can't help picturing outstanding former players lined up in a miles long bread line and waiting for an incredibly long time until finally the Hall of Fame Committee finally comes out tosses a very few loaves of bread, throws a few crumbs to the some of the rest and then slam the door for another year.
There is most definitely a backlog! But it's a self inflicted problem that could be easily remedied simply by increasing the number of candidates admitted each year. The selection of players like Gale Sayers, Doak Walker, etc, established that a player can be recognized for a great but relatively short career. Fans and Hall of Fame voters shouldn't try and reinvent the wheel by now deciding there needs to be a more rigid longevity requirement that didn't exist in the past. Nor should the expediency of dealing with a backlog of candidates be allowed to overshadow the mission of the Hall of Fame...which is "to honor the heroes of the game, preserve its history, promote its values and celebrate excellence EVERYWHERE". The mission and values are worthy ones and they should be upheld.
* It seems like anytime somebody is applying the "longevity argument" with regard to Terrell Davis, they always understate his achievements
 from a wikipedia article on legal precedent
[2} from the "Hall of Fame Mission, Values & Vision" section on profootballhof.com