I applied for a credit card offer, requesting a balance transfer of $5,000. They mailed my card, account agreement, and only approved a $1,000 credit limit and an $800 transfer. Given those amounts, I don't want the card, but the credit union says I can't

You should contact the credit union as soon as possible and discuss your options. 
If you recently received notice of your credit limit and the rest of the account-opening disclosures, you may be able to cancel the balance transfer. The credit union is required to give you a chance to decline the balance transfer once you learn your credit limit and receive the rest of the account-opening disclosures. Generally, you have at least 10 days after the credit union sent the account-opening disclosures (not the day you received them) to call the credit union and stop the balance transfer.

If you did not contact the credit union in time and the balance transfer was made, you will need to pay off the entire account balance. Once you have paid the account in full, you can cancel the card.