Can the Fifth Amendment protection against self-incrimination be invoked in a civil deposition?
Assuming it can be, what potential consequences may the invocation have, if any?
If the question asks, "did you do X" where X is or includes a crime that you could be criminally prosecuted for, you can invoke the 5th amendment in refusing to answer that. I have seen that done and seen that objection to the question sustained in court. However, if admitting to X would provide only civil liability, then the 5th would not apply.
At trial, you may also have to take care not to give direct testimony on things that are so closely related that you "open the door" to being required to answer that question. For example, you can't say "I don't owe because I did X" and then expect to not have to answer "So just to be clear, did you do X?"
Also, depending on context, invoking the 5th might cause a jury to view your testimony more skeptically (cpast points out that "For civil cases, adverse inferences based on pleading the fifth are totally okay"), and if that's going to come up you should ask your attorney about whether or not it'd be a good idea strategically.
No, the relevant provision is:
nor shall be compelled in any criminal case to be a witness against himself
Yes, it can but only for potential criminal liability that may relate to the case. You can't use it for civil liability.
You could be precluded from invoking defenses related to the testimony you withhold.