Ideas may or may not be infinite, in my opinion.
With one definition of 'idea', it could be said that ideas are infinite. For instance, if you can simply increase the quantity or multiplicity of some component(s) of an idea to get a new idea, you could create infinite ideas. This begs the question of whether that idea is unique or not.
Assuming our reality (including our consciousess) is part of a consistent system, it is entirely possible that unique ideas are limited in quantity. This is analogous to how there is a limited number of permutations in a set.
Imagine you have several balls. You may think there is an infinite number of three dimensional configurations, but is it really relevant to speak of infinitely small differences in position that affect the configuration quantitatively, but not qualitatively?