Do Americans "gee things up", or is it just a British usage?

Solution 1:

Answering as a 40-yr old American, I can say that no, this usage is not familiar to me.

It does remind me of a similar expression, "gee-yup", shortened from "giddy up" or "giddyap", an expression used by cowboys to command the horse to begin to move, or to move faster.

In this sense, it is most familiar to me as an expression used by parents to goad children, such as "Come on, gee-yup, or you'll be late for school." (Frequently has the opposite of the desired effect.)

Solution 2:

I believe that gee up is short for ginger up, meaning to cause a horse to run round in a lively manner by shoving ginger up its fundament, and by extension encouraging a person to behave in a lively manner, (one hopes by other means).

If that is the case, then according to this source here, the usage was originally British.

But it goes on to mention that the phrase disappeared from general usage for a long time (a shortage of ginger, perhaps?), to reappear in America in the 1890s. It speculates that the reappearance may have been related to gin up, as Tom Au says, derived from engine.

More here, including rather more than you want to know about feaguing up horses.