Litmus is a weak acid, with a $\mathrm{p}K_\mathrm{a}$ of about 6.5.
Alcohols are extremely weak acids, with $\mathrm{p}K_\mathrm{a}$'s (typically) around 17.
The litmus itself is a much stronger acid than the alcohol. Dissociation of the alcohol won't produce enough protons to shift the equilibrium between the two colored forms of the indicator, so you'll see no color change.
