Hi Fred,
Holy week will be busy. That said walking in 2012 I never failed to find a bed, even in Logrono on Good Friday. Many Spanish pilgrims walk at this time and the Semana Santa processions in some cities - Pamplona, Logrono, Seville, Burgos, Leon in particular attract tourists as well as pilgrims. You haven't said where which Camino you are walking or where you are likely to be during Holy Week.
Bear in mind that you cannot make reservations for publicly run Albergues though most private ones will take reservations.
http://www.gronze.com/ is a reliable source of information on which Albergues do accept reservations. If you are thinking in terms of Hotel accommodation then Booking.com is a probably more reliable authority on availability than this forum.
Buen camino