This assignment/delegation has created a "third party beneficiary" in the Dealership. First, I would label my people:
Third Party beneficiary: Car Dealership.
As a general rule, the promisor is able to assert any defense to performing that he may have against the promisee. In this case, Dave is alleging some sort of breach and that he is entitled to keep some of what he owes (basically alleging that the promisee committed some sort of breach). The merits of his claim are obviously an issue up for analysis (but outside the scope of this question). For this reason, he does NOT have to continue performing the contract and is entitled to not pay the dealership.
The dealership, though, still has a cause of action against the promisee, since he could be best classified as a "creditor beneficiary." Further, when someone delegates a duty, the person delegating is still on the hook for performance (unless, he somehow gets the beneficiary to opt him out).