priority claims on future tax revenues

This is probably the least ominous reason for the rush to approve this. In fact, most of the provisions of the new Constitutional amendment and impending Organic Law won't take effect immediately. The spending ceiling only becomes binding after 2020 (however, to bring a 9% deficit to 0.40% in 9 years does require reducing it by 1% per year in the middle of a recession, which will require biting austerity with immediate effect). There's only one provision of the proposed New Article 135 (in Spanish) which will have immediate effect:

Los créditos para satisfacer los intereses y el capital de la deuda pública de las Administraciones se entenderán siempre incluidos en el estado de gastos de sus presupuestos y su pago gozará de prioridad absoluta. Estos créditos no podrán ser objeto de enmienda o modificación, mientras se ajusten a las condiciones de la Ley de emisión.

Credits to service interest and principal on the public debt of the various Administrations will be understood to be part of the expense account of their budgets, and their payment will have absolute priority. These credits won't be subject to amendment or modification, as long as they keep to the conditions of the law by which they were issued.

The emphasised text is what's being added by the amendment.