There are 2 ongoing independence movements in Spain right now: Catalonia and the Basque C.(Euskadi)
Catalonia´s situation is different but in my opinion, Euskadi's separatist movement is losing strength and support. Maybe a few years ago it could have happened but now it´s unlikely. First of all , the ruling party (PNV) in Esuk. is a nationalist party (Partido Nacionalista Vasco) but is willing to talk and negotiate with the central government (Madrid) .In the past thye used to reject negotiation and simply talking, back when ETA(Terrorist group that wanted independence and killed thousands +info here: https://en.wikipedia.org/wiki/ETA_
(separatist_group))was still active. Second of all the independence movement was based on the differences in culture and language between them and the rest of Spain, but also on the economic differences, since the north of Spain is wealthier and more industrialized than the south, that focuses more on agriculture. People from Eusk. thought that they shouldn't be paying welfare to the 'lazy' southerners with their taxes. (Which is what some Catalonians think right now) . So now that we are recovering from the 2008 recession , people have more money and aren´t so resilient to 'share' their money.
In Conclusion, The Basque could try and make a referendum, but if it happens I don´t think the 'leave' would win. Catalonia on the other hand , I would say there is a 50-50 chance.
Hope this answered your questions..