Did the plastic break off? Is the faucet in limbo and useless? Is there a retaining ring, nut, something holding it on there? How about getting a piece of pvc pipe that will fit in the hole there, cut the ends with tin snips, pliers, band saw, jig saw, whatever you have available, to fit in the holes and turn the thing out of there. Or better yet would be a piece of copper pipe, something stronger. Check it out.