In the New Mexico, US do you have to pay someone for work if after completion you do not feel the work is worth the original amount agreed upon. For example a plumber who gives you a quote, finishes the job, but it is not done as good as you would have liked it to be or it wasn’t all that you originally thought it would be or if they took longer than originally indicated, do you have to pay them the full amount or can you hold some back? If you don’t pay the agreed amount what could they do?
If they have done what the contract requires them to do (plumbing) then you must do what it requires you to do (pay them).
If they have not yet fulfilled their obligations, that is, the work is not yet complete, then you do not yet owe them the money (unless the contract provides for progress payments).
If they have breached the contract in a way that causes you damage (in a legal sense) then your owe them for the work and they owe you for the damage.
If you owe them money, they can sue you. If you claim damages, you can raise a counter claim in response to their suit.
With respect to your specific examples:
- "not done as good as you would have liked" - if "as you would have liked" is a term of the contract then they have breached. However, if the contract is silent then if their work is in accordance with the codes and of a "workmanlike" quality then they haven't.
- "wasn’t all that you originally thought it would be" - ditto although I am confused at how "plumbing" can be anything but plumbing - did you think you were getting music lessons?
- "took longer than originally indicated" - unless there was a specific completion date in the contract, providing that the work was done within a reasonable time taking longer then indicated is not a breach.
Notwithstanding, in all cases, as well as proving the breach, you would need to prove the damage caused by the breach.