The first part of the Norte is definitely the most difficult in terms of finding cheap accommodation. There are albergues, but many of them are only open July/August, and most of them don't open before May. If I were in your shoes, I'd aim for the following:
Zarautz (21km) - Gran Camping Zarautz, on the Camino a couple of km before town, has a pilgrim's albergue for 5E
Deba (21km) - Pilgrim's albergue, open year round, donativo; keys from turismo or policia
Zenarruza (26km) - Pilgrim's albergue in monastery, donativo
Next stretch is tough. Gernika (17km) doesn't have an albergue and Lezama (37km) has an albergue but is probably too far (and I don't know if it would even be open). Your best bet might be in Morga, south of the Camino, where the Albergue privado Meakaur has beds for around 15 euros. 944 911 746. That would make for a 23 km day and then...
Bilbao (27km) - Albergue (Privado) Bilbao Aterpetxea, on the far side of Bilbao along the Camino, around 15 euros
From there to Castro Urdiales (around 37km, if you follow the river out of Bilbao) you'll have another empty stretch, unless the albergues in Portugalete or Pobena open earlier than they ever have before. You'll pass through beach towns along the way, so a hostal would be no problem, but there are no super cheap options.
Now, if you aren't obsessed with walking every step, you could take advantage of the cheat many pilgrims use, taking the Bilbao metro from the city center to Portugalete, chopping off an ugly section of the walk and making the distance between Bilbao and Castro-Urdiales more manageable.
Liendo (19km, from Castro) - The polideportivo is available to pilgrims, donativo
Guemes (31.2km) - One of the must-stay albergues on the Norte, donativo
Santander (14km) - 4 or 5 euros
Requejada/Polanco (35km, or 28km if you follow the train-bridge over the river from Boo de Pielagos instead of following the Camino all the way around to the car-bridge) - 4 euros
Santillana del Mar (10.5km) - Why not take an easy day and stay in one of the nicest towns on the Norte (and check out the Altamira Caves)? New albergue opposite the church, 6 euros
Comillas (22.5km) - Another beautiful stopping point with a new albergue (4 euros)
Colombres (29.1km) - The polideportivo is available to pilgrims (2 euros)
Llanes (23.3km) - Lots of hostels, I recommend Albergue La Estacion (around 10 euros). Also recommended is the Albergue Asturias in Playa de Poo, 3km after Llanes (9 euros)
San Esteban de Leces (34.2km) - A nice albergue (4 euros) just off the Camino; a private hostel is available in Ribadesella if you want to pay a little more to go a little less far.
Soon after that, the Camino splits, as does my knowledge of the route (I only know the Primitivo from there on). Hope this helps you make it halfway to Santiago, though! Please let me know if any of the info proves to be inaccurate, or if you find any other good options.
EDIT: Just so I'm clear, there are other places to stay - lots more in the summer - but I think this is the cheapest way to move through the Norte at a reasonable pace outside of the summer.
Dave