I read a book in 1985 that was about Lourdes, in Northern Spain.  The
premise was that the Virgin Mary (who appeared at Lourdes) was going
to appear again and grant 3 wishes so people flocked there, hoping She
would cure them, etc.  But the Basques decided to use this opportunity
to make a political statement and blow up the basilica.  What is the
title of this book?

Hello.

Your book was "The Miracle" (1984) by Irving Wallace.

From a reader review at Amazon.com:

"In THE MIRACLE it has now been almost 130 years since the apparitions
at Lourdes and the Vatican has recently discovered a journal kept by
St. Bernadette in which she recorded three secrets told to her by the
Virgin Mary... Virgin Mary would return during a Reappearance Time and
perform a miracle...
Mikel Hurtado, a member of a Basque freedom organization, has plans to
travel to Lourdes to blow up the grotto in order to make a political
statement and advance the cause of his people. "
http://www.amazon.com/exec/obidos/tg/detail/-/052524266X/

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search strategy:
lourdes "virgin mary" basque "blow up"

Thanks.

I wondered that for 20 years.  Thanks.