It would mean absolutely nothing. All it would mean is that we (living in what we think is year 6000) either miscounted or (those who wrote the medrash) misinterpreted what was going on. Many people have guessed when the mashiach would arrive and been wrong. Consider the division of the ages of the worls into two thousand year epochs in which the birth of Avraham (194

, Yitzchak (204

or Yaakov (210

are considered the end of the first epoch. The dates in such calculations are only approximate.
All we can say is that when someone appears to have met the criteria for mashiach, then we would be willing to accept him. If he fails or dies, then admit that he wasn't and go on. Look at the trouble Shabtai Tzvi and his predecessors for the past several thousand years have caused.
Rambam does not set the time at 6000 years. He says Hashem will send Mashiach when He has determined to. We are guessing about 6000 years. Indeed consider the problem if it actually means 6001 (1 - 1000, 1001 - 2000, ... 5001 - 6000) and people get upset about mashiach not coming in 6000 Or indeed, consider the upset if people are off in when during the year. Chet Haeigel occurred because of a one day miscalculation.
Rambam Hilchos melachim 12:2 says
Regardless of the debate concerning these questions, neither the order of the occurrence of these events or their precise detail are among the fundamental principles of the faith. A person should not occupy himself with the Aggadot and homiletics concerning these and similar matters, nor should he consider them as essentials, for study of them will neither bring fear or love of God.
Similarly, one should not try to determine the appointed time for Mashiach's coming. Our Sages declared: 'May the spirits of those who attempt to determine the time of Mashiach's coming expire!' Rather, one should await and believe in the general conception of the matter as explained.
There is a quip that the prohibition did not stop the Rambam from speculating.
As it says
When Will the Mashiach Come?
There is a wide variety of opinions on the subject of when the mashiach will come. Some of the Jews' greatest minds have cursed those who try to predict the time of the mashiach's coming, because errors in such predictions could cause people to lose faith in the messianic idea or in the Torah itself. This actually happened in the 17th century, when Shabbtai Tzvi claimed to be the mashiach; when Tzvi converted to Islam under threat of death, many Jews converted with him. Nevertheless, this "prohibition" has not stopped anybody from speculating about the time when the mashiach will come (including some who themselves spoke harshly of those who engaged in such vain efforts!).
Although some scholars believed that God has set aside a specific date for the coming of the mashiach, most authorities suggest that the conduct of mankind will determine the time of the mashiach's coming. In general, it is believed that the mashiach will come in a time when he is most needed (because the world is so evil), or in a time when he is most deserved (because the world is so good). For example, each of the following has been suggested as the time when the mashiach will come:
- when all Israel repent a single day
- when all Israel observe a single sabbath properly
- when all Israel observe two sabbaths in a row properly
- in a generation that is totally innocent, or totally guilty
- in a generation that loses hope
- in a generation where children are totally disrespectful towards their parents and elders (commonly thought to be "our generation", in every generation!)