Most of the speculation that quarks might not be fundamental, I think, flows directly from the fact that there are so many different kinds of quarks and that they show a certain periodicity that shows clear patterns of charge and mass, to which there are various formulas (see elsewhere in PF for the post on this) which could plausible suggest a relationship.
When we have seen these kinds of patterns before (e.g. in the particle zoo that preceded the discovery of quarks, and in the period before we discovered the proton-neutron theory of the nucleus), this kind of pattern always turned out to be evidence of substructure. The inference is, that the current pattern might also be evidence of substructure, and string theory is one theory that seems to show what that kind of substructure might look like.
For example, we currently have three "orders" of spin 1/2 particles, the "electron" order, the "mu" order, and the "tau" order (with corrosponding higher order electrons, neurinos and quarks. One could easily propose the entirely plausible theory that there is also a fourth "order" of spin 1/2 particles each with masses a couple of hundred times those of the "tau" order particles, that they decay very rapidly to lower order particles, and that we haven't observed them yet because our particle accellerators don't have enough juice. Indeed, if I wanted a real big particle accellerator, I might spend a good deal of time talking about the theory and I wouldn't even be particularly dishonest in doing so, because the most massive "tau" particle does have an suggestive closeness to the largest particle we have been able to detect.
The fact that the higher order quarks "decay" while this may simply be a product of deceptive use of language, is also evocative of the idea that quarks are not fundamental.
The article, suggests theoretical underpinnings for a composite Higgs particle:
http://arxiv.org/ftp/hep-ph/papers/0209/0209082.pdf
"Understanding the Genesis of Mass" by George Triantaphyllou
We give a pedagogical and concise presentation of dynamical mass generation involving strongly-interacting mirror fermions. As a paradigm which has been explicitly shown to predict correctly the weak scale and the weak angle and thus addressing successfully the essence of the hierarchy problem of energy scales (contrary to "supersymmetric" or "extra-dimension" models) and the unification of fundamental forces, it might have already manifested indirectly its validity experimentally, as first noted by the author in 1998, via the bottom-quark forward-backward asymmetry and the related coupling parameter A_b. After a decade during which the particle-physics community was frequently misled by a particularly obscurantist interpretation of the L.E.P./S.L.C. precision data, this approach emerges as a strong candidate for new physics beyond the standard model of elementary particles to be thoroughly tested in the forthcoming high-energy experiments. 
