What penalties would Westerosi nobles suffer if they were to refuse a call to arms from their corresponding Warden? Could Jaime Lannister have done anything if, during his tenure as warden, he raised banners and the eastern lords ignored him?

See here. 

Now, Jaime would have an unusually difficult time because there would be the argument raised against him that he wasn’t the rightful Warden of the East, that the lords of the Vale were of course ready and willing to answer the call from an Arryn, etc. etc.