What does “As for Romney, the G.O.P. is over him” mean?

Solution 1:

To "be over (someone)" is an idiom that means a relationship is finished. For example:

I'm so over him!

I believe it comes from this definition of 'over':

11) having recovered from the effects of she's not over that last love affair yet

So in the particular example, it means that the GOP is no longer enamored with Romney. The fairy-tale-like relationship is over.

Solution 2:

I think it means that the GOP is done with Romney-- no longer interested in what he has to offer. Source: Native English speaker.

Solution 3:

I've upvoted @ahannon14's answer, which is essentially correct. From OED:

over 13: With reference to duration, repetition, completion, resumption, etc.
a. Past, gone by, finished, at an end. See also all over.
b. over and done with (later also over with)
finish with, have done with (esp. something troublesome or disagreeable).

The usage simply extends the "core" literal meaning

over = above
to metaphorical
over = beyond [in time, i.e. - past]

The GOP have largely gone beyond, or gotten over Romney. As a cynic, I might say it means they've discarded him because he's of no further use. But I'm sure the intended meaning is that in the recent past they were upset about Romney (because he lost); now they're over and done with [their regrets over having backed a losing candidate].