Same here, though my husband would not pay at all.

It's definitely going to depend on how shitty the job was. Most of the time, I'm still going to pay, but if we're talking something really expensive like carpet work and the person fucked it up to the point where you're actually going to have to go and REPAY someone else to do the job, then I would totally be telling the person that I cannot pay them for a job they did not do correctly. I'd calmly explain that they screwed it up and instead of paying them for an F up, I'm going to need to keep the money they did not earn to pay someone who'll do it right. Of course I wouldn't be that hateful, but I would tell them that I need to keep the money to pay someone who'll do it right.

How bad was the job?

There has only been one time in my life where I've not paid for someone's job. My dentist. I paid him in full (the portion out of pocket that my ins. didn't cover) on the same day of my root canal therapy treatment. He didn't finish the root canal therapy that day, and a year later, here I am with only half the damn root canal when I paid in full. He told me to come back so he could fill some teeth and finish the root canal. I did. When he said "all done, and sorry I ran your ins. out so you only got temp. fillings. And informed me that I'd need to make an appt. to fill the 3 teeth permanantly in less than 5 weeks as well as make an appt for the rest of my root canal, that is when I walked out of the office with the money in my pocket. Got a letter today sayin' they've sent me to a collection agency, but that dentist fucked me up! So that is where you have to draw the line. When the person who's supposed to be qualified for your carpentry (or dental work!) does you more damage than good, more damage than you started with, and only left you having to pay all over again for someone better to do the work, then you need to draw the line. Simply because you don't pay for a service that has left you with real problems like a carpet that needs re-done, or teeth that need re-fixed. You have to stand up for yourself. Perhaps even, I hope anyway, a worker like this will have their mistakes brought to their attention and be less likely to screw someone else over.

Ever considered also writing a review on the company who screwed your carpet? If they intentionally done a shitty job and aren't cooperative in your decision to withdraw your payment to them, it's not a bad idea to give others a heads up. I did this with my dental issue online because my ins. company said that it needed to be noted that this particular dentist was not a good recommendation. You may even consider that if they give you more problems.

But, what I'd do at this point, if you haven't already, is bring it to their attention that the job is not properly done and ask if you can make arrangements to either have the company send someone else to re-do (without charge!) or give you a refund to have someone else do the job.

I would refuse to pay if I wasn't satisfied.

I'd probably still pay, but first I would attempt to negotiate. Then, I'd probably threaten some court action or bad publicity.