After making the above comment I did a quick Google search and found a paper entitled "Kolmogorov Complexity and Computational Complexity" by Lance Fortnow. The paper is about resource-bounded variants of Kolmogorov complexity. After giving the standard definition and some consequences he writes the following.
Of course this definition of Kolmogorov complexity makes any complexity theorist cringe: what good is a small program [for] $x$ if it takes the life of the universe to produce $x$?
Perhaps he could give you more precise pointers to the literature.