They'd have to do it gradually to avoid all the 'Republicans are throwing people out of work talk', rely on attrition and early retirements, inter-department transfers etc.Dept. of Education created: 1979, and began operating in 1980.
Republicans have been pledging to eliminate it since 1980 and submitting bills to eliminate it not long after.
It would be great to see, but this history causes me to keep my optimism in check.