Theoritically game can go on forever, until one side scores!
If the score is tied after regulation time has concluded, an additional 15-minute period is played. The captains meet with the officials for a coin toss, and then one side kicks off to the other, as at the start of a game. The first side to score by any means wins. In the regular season, if the overtime period is completed without either side scoring, the game ends in a tie. Because there cannot be a tie in the playoffs, the teams switch ends of the field and start additional 15-minute overtime periods until one side scores.

1. The sudden death system of determining the winner shall prevail when score is tied at the end of the regulation playing time of all NFL games. The team scoring first during overtime play shall be the winner and the game automatically ends upon any score (by safety, field goal, or touchdown) or when a score is awarded by Referee for a palpably unfair act.

2. At the end of regulation time the Referee will immediately toss coin at center of field in accordance with rules pertaining to the usual pregame toss. The captain of the visiting team will call the toss prior to the coin being flipped. 3. Following a three-minute intermission after the end of the regulation game, play will be continued in 15-minute periods or until there is a score*. There is a two-minute intermission between subsequent periods. The teams change goals at the start of each period. Each team has three time outs per half and all general timing provisions apply as during a regular game.

Disqualified players are not allowed to return.
*Exception: In preseason and regular season games there shall be a maximum of 15 minutes of sudden death with two time outs instead of three. General provisions that apply for the fourth quarter will prevail. Try not attempted if touchdown scored. If there is no score in the 15 minutes, the game shall end in a tie.

I think if we were doing college football overtime rules, it takes a long time for a person to score. The rule in college is one team scores wins and if the other team scores, it the second overtime. The overtime keeps going until someone wins or the other team does not score. The only thing for college football is each team starts at the 30 yard line.

The most recent playoffs tie game is : http://www.mahalo.com/Colts_Chargers

Check out the NFL youtube video I have included below talks about the first ever Sudden Death overtime game in the history of Football:
Source(s):
http://www.mahalo.com/Colts_Chargers
http://en.wikipedia.org/wiki/1958_NFL_Championship_Game
http://www.profootballhof.com/history/release.jsp?release_id=1805

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