For a (reductive) group G, let O (K; G) be the ring of functions on the variety of G-representations of the fundamental group of the complement of a knot K in $S^3$. There is an algebra map from the spherical double affine Hecke algebra H^+(G; q=1,t=1) to O(K; G), which leads to the question "does O(K) deform to a module over H^+(G; q,t)?" We give a conjectural positive answer for G=SL_2(C) and discuss some corollaries of this conjecture involving the SL_2(C) Jones polynomials of K. This is joint work with Yuri Berest.