Carefully check your agreement with Wells Fargo, including all the addendums they may have sent you over the time youve been their customer. Federal law states that they must notify you of changes to your agreement at least 30 days in advance of the change, and that you have 30 days after the notification to refuse the change.
When you refuse a change to the terms of your account, you are technically closing your account. You still have the right to make periodic payments on the account and you do not owe the full balance immediately, so long as you aren't over the limit or late on any payment. You also cannot use the card again for any reason, because the bank will interpret that as you reopening your account and you will have then agreed to their change.
None of this may matter, though. Most banks that issue credit cards made changes to the accounts several years ago and tied the interest rates to certain indices, where when the prime rate changes, your rate changes with it. Most card issuers also reserved the right several years ago to change the spread (difference between your rate and their chosen index) when they perceive you as an increased credit risk, or if you miss payments or go over-limit.
My advice to you is carefully read your card agreements including all the amendments they have sent you over the years. If you find that they have raised your rate legally, you would certainly want to pay down your most expensive balances first. You may also want to contact them to ask for a reduction in your rate. Most companies will reduce the rate in order to keep payments coming, rather than risk being cut off.