The Masseneinwanderungsinitiative passed in 2014... and fuck all happened (despite the no campaign heavily leaning on the argument that it would kill the bilaterals, e.g. https://www.emuseum.ch/internal/media/dispatcher/286887/full). When push comes to shove, there is a solid bloc in parliament and the executive for saving the EU bilaterals, even if it means ignoring constitutional initiatives.