Constitution Amendments made effective :
The Constitution Amendments have been made notified and made effective. These were made partly effective on 12-9-2016 and fully effective from 16-9-2016.
Section 19 of Constitution (One Hundred and First) Amendment Act, 2016 allows one year transition period of one year for switching over to GST. Thus, in any case, GST has to be in place before 16-9-2017.
Of course, Section 20 of Constitution (One Hundred and First) Amendment Act, 2016 empowers President of India to issue order for removal of difficulties. This power includes adaptation or modification of any provision of Constitution. Thus, in extreme situation, this deadline can be extended.
Even otherwise, entry 97 of List I of Seventh Schedule to Constitution empowers Central Government to impose any tax not specified in List II and List III. Thus, technically, Central Government can even impose any tax (even GST) without concurrence of State Governments or GST Council.