There are a few teams in history that we can draw some apt comparisons to this FSU football team.
2005 USC: The Trojan's winning streak hit 34 games between 2003 and 2006 (bowl game for 2005 season). USC lost to California 34-31 on September 27, 2003. They won out for 2003, heck they even try to claim a national title when they did not play in the BCS Championship game. They earned the BCS National Championship (undefeated) in 2004 with a 55-19 slaughtering of Oklahoma. The Trojan's then had an undefeated 2005 season before losing 41-38 to a Vince Young led Texas team in the Rose Bowl for the National Title.
2002 Miami: The Hurricanes winning streak reached 34 games between 2000 and 2003 (2002 Bowl game). Miami lost at Washington 34-29 on September 9, 2000. They ran the table to complete the 2000 season. They won a BCS Championship the following January with a snoozer win over an over-rated Nebraska team 37-14. Miami then ran the table in the 2002 season before losing 31-24 to Ohio State on a very controversial call.
**BONUS: The above two examples share a few more similarities. Both USC and Miami only end up with ONE NC for a 34 game winning streak. Both ended up losing to power programs that WERE LONG OVERDUE for a NC. Texas had last won a NC in 1969. Ohio State had last won a NC in 1968. Both had perhaps their greatest QB of all-time at the helm and both were littered with future NFL starters.
1992 Miami: After winning NCs in 1983, 1987, and 1989, the Canes were re-building in 1990. They started a winning steak that hit 29 games. They dropped the opener at BYU (28-21) and then lost at Notre Dame (29-20) on October 20, 1990. They reeled off 6 in a row (including the infamous beatdown of Texas in the Cotton Bowl), ran the table for a NC in 1991, and were undefeated in the regular season of 1992 before losing to Alabama 34-13 in the Sugar Bowl. The Crimson Tide had won a NC in 1979 and 1978 so not quite the same time period of the first two examples and the "overdue" power program. Still some similarity.
Alabama 1993: The Tide lost at Florida 35-0 on September 14, 1991. They reeled off 10 wins to finish the 1991 season, went undefeated in 1992 (beating Miami 34-13) and won their first 5 of the 1993 season before tying Tennessee 17-17. The Crimson Tide got two more wins before the bottom fell out of the 1993 season where they lost three of their last five (LSU, Auburn, Florida).
Nebraska 1996: The Cornhuskers did their 26 game winning streak the right way, garnering two titles out it. Nebraska lost the 1993 season bowl game to Florida State 18-16 in the Orange Bowl. They ran the table in 1994 (beat Miami in Orange Bowl), ran the table in 1995 (beat Florida) before losing to Arizona State 19-0 in week two of the 1996 season.
This is the "company" that FSU currently resides in. These are without question some of the best teams and "era's" of college football history.
Some other tidbits about this winning streak:
The University of Florida has NEVER had an undefeated season. Never. A different way of looking at that is that the Gator's have NEVER fielded what would be considered a "historically" great team (the first cut is eliminating the NCs who did not go undefeated). You may feel free to remind your UF brethren of this simple fact as often as you like. (Bonus: always a good time to remind at times like this when they are looking for a Head Coach and talking about what a "premier" program they are)
The University Oregon----currently ranked ahead of FSU----has never gone undefeated. Heck they have never even won a National Championship. Double heck, they have only played for it once. Yet they are better? Wow..........
Oklahoma has the nations longest D-1 winning streak at 47 games (1953-1957). That earned them two NCs. FSU would need to win out through September 2016 to take that record. Long way to go and that is why that record may be the toughest to break in college football. Having said that FSU is now well over half way home and it can't be discounted that Miami/UF are a mess right now and that can't hurt.
FSU is trying to win back to back NCs. The programs that have done it:
Alabama (2011, 2012)
Nebraska (1994, 1995)
Oklahoma (1955, 1956)
Notre Dame (1946, 1947)
Minnesota (1940, 1941)
*The above are CONSENSUS National Champs