In an ordinary negotiation, each side has things it wants, while it dislikes some or all of the things the other side wants. A union wants higher wages for its workers, while the company doesn’t want to pay the higher wages. You’d rather have your partner do the laundry while you do the dishes, but your partner doesn’t like doing the laundry either. The White House wants to increase taxes on the wealthy, which Republicans don’t like, while Republicans want cuts to social programs, which the White House doesn’t like.
But the debt ceiling is something entirely different. In this case, what Republicans want is the ability to plunge the country into a financial catastrophe, making life miserable for who knows how many Americans. That’s what they want. Seriously. You might say, well, all they actually want is the ability to threaten to plunge the country into a financial catastrophe so they can extract concessions, but the threat would be meaningless unless they were willing to follow through on it. So if you wanted to be generous, you could say that what Republicans want in this particular aspect of the negotiation is to maintain their ability to credibly threaten to plunge the country into financial catastrophe.