"An end (ajal )is fixed for every people( ummah). When their appointed end-time is come there shall be neither a moment’s delay or haste." - Qur’an 7:34 , 10:49

"To every people (was sent) a messenger: when their messenger comes (before them), the matter will be judged between them with justice, and they will not be wronged." - Qur'an 10:47

"For every Ajal ( end ) there is a Book. He abrogates or confirms whatsoever He wills, for with Him is the Mother Book." - Qur’an 13:38-39

"For every message is a limit of time, and soon shall ye know it." - Qur’an 6:67

Regarding the Hadith below: Both Sunni and Shi'ah sources have reported this particular Hadith, however, it is not considered to be a Sahih Hadith, thus absent from the Is’hah of Bukhari, Muslim, etc... However, this Hadith can be found is other books. For example:

In the book of Najm'us-Saghib, Haji Mirza Husayn-i Noori the well-known Shi'ah scholar and commentator writes:

"At the time of the revelation of this verse ("li-kulli ummatin ajal") which suggests that for every nation a term has been established, they asked the Messenger of God what is the term for the ummah of Islam, and He replies: `If my people [i.e. Muslims] were truthful they remain for one day. If they degrade, half a day* will they last." [Bihar'ul Anwar, Vol 13]" - Najm'us-Saghib p. 87

* A "day" can have different values according to the Qur'an ( see for example 32:4 ), but which ever value we choose, the fact remains that it is a set time.

One can also argue that the set term for the Muslim Ummah, is the Day of Judgment. This too is a valid argument.