And The Donald has now given us the definitive answer:
Grabbing Our Pu$$y
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I’m sure a few years from now I’ll be able to laugh at that. It really SHOULD be funny, but somehow, I just can’t right now. . . 
Grope Others’ Pussies.
I really want to use the word “opportunistic” in there, but I can’t seem to make it work. . .
There’s barely even a D, in the Ol(d[e]/’) part I mean.
Gone Off Prozac
Should be changed to POP. Party of Pepe.
Awesome!
Gang of Psychos.
At both the Bangkok Post and The Nation English-language dailies in Thailand, the style is to all-cap an acronym if you pronounce each letter such as HIV and only cap the first letter if it’s pronounced like a word such as Aids or Nato. I recall this one Brit at the Post, we had to convince him it really was pronounced G-O-P. He insisted it must be pronounced “Gop” and was intent on rendering it that way.
Grotesqueries On Parade.
Greasy Old Perverts.
Grumpy Obnoxious Politicians.
Greedy Opportunistic Panderers.
That’s better than whatever pussy-related one I was going to come up with.
I clicked on this thread thinking it was going to be that the GOP doesn’t stand for anything, eg they have no actual values or beliefs any more other than get in power and block anything the Dems try and do. That would have been a decent pit thread as well.
But sometimes simple is best “Greedy old pricks”… slight variation of some of them above.
Got Our Panties (Inna Bunch)
Surely in some quarters the G.O.P. is “God on Politics.”
Uh… Globally Opportunistic Partisans?
Groin Ogling Perverts?
Green Oozing Pustules?
Germanys Old Practises?
This. They no longer stand for anything.
That’s certainly the answer this week.
No one has put forth
G aslight
O bstruct
P roject?
Good Ole Pedophiles
Straightforward contemporary meaning:
Government Obliteration Party