Anyone who endangers others by driving under the influence ought to be punished quite severely, and NFL players are no different. Set aside they are role models, wealthy enough to pay a driver and certainly shouldn't be drinking quite that much in-season anyway in the interest of peak performance, they are still endangering themselves and others. That should simply not be allowed.
Yes, the NFL should issue harsh penalties to players arrested for DUI. DUI is a serious issue--and, by the way, illegal! Unfortunately, many people, including law enforcement, do not take it seriously. The NFL should issue penalties for DUI that are at least as harsh as for other illegal acts.
The NFL has at any given time a number of 'bad boys' that are in trouble with the law for one thing or another. The NFL is also experiencing a leveling off or down turn in viewership. One sure way to get more negative attention is if one of these players to get drunk, get in their car and run someone over. If that happens, the negative press will only increase and that is not something that the NFL needs.
The NFL should issue harsh penalties (fines and suspensions) to players that are convicted of DUI. No one should ever drive under the influence--no matter how rich and famous that person is. Athletes should be held accountable for drunk driving. The NFL can play a leadership role in cracking down on this dangerous behavior.