Is it an act of Shirk to be pessimistic regarding days of the week?
If an Imaam does this, is it permissible to pray behind him when he leads prayers?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Being pessimistic in terms of certain days, seeing birds and the like is considered an act of Shirk (polytheism) and distrust in Allaah The Almighty. Therefore, anyone who thinks that pessimism brings benefit or wards off harm actually believes in evil omens. Therefore, he associates others with Allaah The Exalted in worship, because he believes that other than Allaah The Almighty can bring benefit or ward off harm. Ibn Mas'ood narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said that pessimism is an act of Shirk which a believer can treat by relying upon Allaah. [Ahmad, Abu Daawood and Ibn Maajah]

Thus, anyone who feels such pessimism in his heart should ward it off by having complete trust in Allaah the Almighty and depending on Him. He should also say: "Allaahumma la khayra illaa khayruk, wa laa tayra illaa tayruk, wa laa ilaaha ghayruk" (O Allaah, there is no benefit but from You, there is no will or decree but Yours, and there is no god worthy of worship except You)"  [Ahmad]

If this Imaam is pessimistic regarding days of the week and  believes that other than Allaah The Almighty can benefit or harm and acts accordingly, by  either refraining from certain acts or proceeding with them, then this is a plain Shirk.  Therefore, praying behind him while he leads prayers is impermissible as the Prophet, sallallaahu ‘alayhi wa sallam, said that whoever lets pessimism refrain him from proceeding in an act has fallen into Shirk [Ahmad]

However, if this pessimism is no more than a feeling in his heart or an idea that crosses his mind without actions, then it is not considered an act of Shirk because very few people are safe from such ideas.  Ibn Mas'ood mentioned that everyone experiences such ideas, which was interpreted by Al-Khattaabi by saying that  all hearts experience pessimism, but Allaah The Almighty wards it off by guiding a person to rely upon Him.

Allaah Knows best.