An important property of a superconductor is its critical current density (i.e. the maximum current density it can carry while still remaining a superconductor). This is a particular problem for superconducting magnets since the critical current density decreases in the presence of a magnetic field. While high temperature superconductors exist (~110K) they don't have the critical current densities needed for magnets producing 13 Tesla fields where as for low temperature metal superconductors (e.g. Nb3Sn) it is just about possible. People are talking about using high temperature superconductors in Maglev trains some time in the future but the field strengths would be a lot lower than a tokamak. It should also be noted that because of all this the generally held notion that if we could get a viable fusion reactor working it would be perfectly safe is probably wrong. A full scale tokamak that produced useful amounts of energy would be huge (football stadium size) and hense the associated magnetic field would not only have a very large field strength but would encompass a massive volume. Playing around with the equation E = B^2.V/(2mu) you should be able to convince yourself that the energy stored in the field would be enormous and therefore a magnet coolant failure could be catastrophic.
The existing limits on current density in HTS superconductors are not fundamental, and I suspect they'll improve by quite a bit. (Typical high-Tc wire these days, due to manufacturing limitations, is actually made mostly of silver and other metals, with only a little bit of superconducting material. The other stuff is added for mechanical strength.)

I'm actually not a big fan of fusion research, but for other reasons...

Experiments at Purdue with sonofusion looks promising. Unlike tokomats the strong magnetic fields are not needed. Unlike claimed cold fusion experiments no precious metals are needed. Hot fusion research is a lost cause. They have had over 50 years of experiments behind them and have only produced arguments for more government grants.