Answer
Nebraska did. Michigan was awarded the AP #1 spot by a bunch of sports writers after an extremely unconvincing, controversial 21-16 Rose Bowl win over a weak #7 Washington state team. #2 Nebraska absolutely raped #3 Tennessee the following day 42-17 and got the coaches poll #1 as they should have. AP writers just had to give it to Michigan because Nebraska had been National Champs 2 of the previous 3 years, proving that the writers for the AP poll were completely incapable of objectively awarding the National Championship to the BEST TEAM. The next year... we get the BCS.
To further clarify BrodyDanger's incredibly biased answer above: at the end of the 1997 football season and bowls, Nebraska received 32 1st place votes in the Coaches' Poll and Michigan received 30. In the AP Poll, Michigan received 51.5 votes and Nebraska 18.5. However, Michigan was ranked consensus (i.e. both polls) #1 going into the Bowl season. Officially, the two teams were co-champions.
These are all the organizatins that credited each team as National champs... Notice the much larger list for the Coaches Poll team
1997Michigan12-0Lloyd CarrAP, FN, FWAA, NCF, NFF, SNNebraska13-0Tom OsborneA&H, AS, B(QPRS), BR, CCR, DeS, DuS, ERS, MGR, NCF, NYT, R(FACT), SR, USAT/ESPN