The Nealder-Mead algorithm is meant to be used for low-dimensionality problems. fminsearch uses it.
 Lagarias, J.C., J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions," SIAM Journal of Optimization, Vol. 9 Number 1, pp. 112-147, 1998.
for more details.
So using it for 1275 is probably a very bad idea. How long it will take is very difficult to say beforehand. It depends on the computational complexity of evaluating your cost function. It also depends on your response surface. If is is smooth, then it might converge reasonably fast, if it is complex, it might get stuck calculating forever. Anyway, it will more likely get stuck in a local optimum than actually find the global optimum. It is likely that you would end up waiting longer than the age of the universe.