To even get invited to New York, you have to have outstanding stats and be on a great team. RGIII's win last year came from one of the "worst" teams for a Heisman winner in quite awhile:
Top three in recent years with final ranking and team losses:
2011 - RGIII (#12, 3 losses), Luck (#4, 1 loss), Richardson (#2, 1 loss)
2010 - Newton (#1, 0 losses), Luck (#4, 1 loss), James (#2, 0 losses)
2009 - Ingram (#1, 0 losses), Gerhart (#21, 4 losses), McCoy (#2, 0 losses)
2008 - Bradford (#1, 1 loss), McCoy (#3, 1 loss), Tebow (#2, 1 loss)
2007 - Tebow (#12, 3 losses), McFadden (#25, 4 losses), Brennan (#10, 0 losses)
2006 - Smith (#1, 0 losses), McFadden (#12, 3 losses), Quinn (#11, 2 losses)
2005 - Bush (#1, 0 losses), Young (#2, 0 losses), Leinart (#1, 0 losses)
2004 - Leinart (#1, 0 losses), Peterson (#2, 0 losses), White (#2, 0 losses)
2003 - White (#3, 2 losses), L. Fitzgerald (#26, 4 losses), E. Manning (#17, 3 losses)
2002 - Palmer (#5, 2 losses), B. Banks (#3, 1 loss), L. Johnson (#10, 3 losses)
So in the last 10 years, only two guys have won it with more than two losses (RGIII and Tebow); everyone else was ranked in the Top 5. And only six others made the top 3 with more than 2 losses.
You have to be on a top team or have unbelievable stats to be in contention.