The BJP wanted to bring Jagan into its fold by offering this post to him. There is a second reason for this. Both the Janata Dal United led by Nitish Kumar and the Shiv Sena have been asking for this post. Both the allies are important as there are elections in both Maharashtra and Bihar in quick succession. Also, both the parties have considerable number of seats. In fact, Shiv Sena is the oldest ally of the BJP. So, choosing between the two would have been a difficult task for the BJP. Hence, the BJP wanted a third party, YSRCP in this case, to take up the post so that the issue could be amicably resolved.
However, the YSRCP has decided not to take the bait. There are two major reasons for this. Firstly, the post is not so very important. There is no real power vested in the deputy speaker's post. Secondly, by taking up the post, the YSRCP would send signals that it is part of the NDA. This would give a stick to Chandrababu Naidu to beat YS Jagan and the YSRCP. Hence Jagan has wisely decided not to take up the post.