I'm in a very similar situation. I'm travelling outside the US and citibank blocked my online access and want my ATM or debit card number to let me through. I don't have them with me, I have only a citibank credit card with me.
So I called them 2 times and they say they can't do anything except send me a new debit card number. But I'm travelling in different locations and can't stay in the same location for long time to wait for the debit card to arrive.

I've been a citibank customer for 4 years and from the first day they gave me headache, blocked my access and cards multiple time and were not pleasant and convenient to work with. That's it. When I come back from my vacation I'm closing all my citibank accounts. <redacted by moderator> them and <redacted by moderator> their 2% cashback. I will better get 1.5% cashback from Chase or some other bank, but avoid working with the bank that gives me so much headache and trouble.

For other poor citibank customers with similar problems I can recommend Chase. They are not perfect but I like them more than citi or bofa.