Is it possible to negotiate with credit card company for a repayment plan?

Yes, you can do so. Besides, you can choose to settle your debts with professional help. But that would put a slight ding on your credit. Whatever you choose, just make sure you do it in writing. Moreover, if you're working with a professional, then make sure your debts are settled as per FTC's rule:

Yes, you can call your creditor and negotiate a repayment plan. You can negotiate terms, interest rates, and payments on your credit card debt if you’re really finding it hard to pay off your credit cards.

Yes, you can get a repayment plan. But, before requesting to your credit card company, it's recommended to calculate how much debt you owe and how much you can afford to pay off. After doing this, be ready with a better answer, mentioning your present financial hardship. See, only giving the reason is not enough. The reason can be granted as an excuse. So, you should mention the proper explanation behind the financial disaster.

If you feel you're unable to do this, then contact a settlement company; they can negotiate on your behalf.

You can talk to your credit card company for a workout arrangement wherein the bank lowers or eliminates interest rate and minimum monthly payment; it may also stop assessing the late fees. However, your credit line may get reduced; as a result of which, your credit utilization ratio will increase thus lowering your score to some extent.