My pasta doughnut is very stiff. Is there any way to save it?

It may not make Italian style cut pasta, but Hungarians and Eastern European Jews have a pasta they call Egg barley, Farfel, or csipetke (pinches). Cut the dough into small sections just so it's easier to handle, and, using a pinching motion, pluck off little irregular shapes about the size of Israeli couscous. Place a tea towel on a sheet pan and spread the little dough pieces in an even layer. Let dry at room temperature, or place in an oven on its lowest setting. They should be dry and hard. Store in a tightly sealed container. They will keep like any dry pasta.
To cook: add to broth to make soup, or to stews; simmer until soft. You may need to add additional liquid. We would also cook them for the starch side for a meal. To a large saucepan, heat 1-2 Tbs of neutral oil. Add the desired amount of pasta and stir over medium heat until starting to brown. Take off the heat and add 1 2/3 cups water or broth for each cup of pasta. Careful! It will steam!
Return the pot to the heat and bring to a low simmer. Cover and let cook for about 15-20 minutes or until tender; add more water if needed, but the water should be all absorbed, and the end product should be moist but not soupy.
Good luck! You got this.

"Pasta machine"? As in a digital box that makes pasta? I'd just toss this batch (if its overworked, there's not much that can be done about that), make another by hand, give it a quick 30 minute rest and roll it out with a rolling pin. A bit of elbow grease, but so worth it.

It really shouldn't need any more than an hour to rest, so I'd cut my losses. Chock it up to experience.

I meant pasta dough. Autocorrect got the best of me