UPDATE: Spurred by a lively discussion on Julia's Facebook page about this, I actually finally got raw quantitative data (as opposed to "my reading of the literature is..." or "I talked to a philosopher who told me that...") pertinent to the issue at hand.
According to the Philosopher's Index, the most comprehensive database of philosophical entries (covering 1940-2010), 2052 articles published in English over the past 70 years include the word "intuition" in the abstract. This, arguably, is an overestimate as far as this discussion is concerned, since not all these papers actually deploy philosophical intuitions as a major part of their arguments.
Still, this is out of a total of 234,018 papers, which means 0.88%. I think that any claim to the effect that intuition plays a "major" role in the philosophical literature runs into trouble, given these statistics.
Out of further curiosity, I inquired about the possible differential frequency of the use of the term intuition in abstracts taken from different sub-fields of philosophy. Here is the breakdown (the total doesn't add up to 2052 because there is a fairly significant "miscellaneous" category):
461 in ethics
417 in epistemology
385 in metaphysics
276 in logic
190 in philosophy of science
100 in semantics
46 in political philosophy