It takes about 2-3 weeks to handle the refund on the e-file processing, although the IRS can hold your return for a variety of reasons (identity verification, earned income credit eligibility checking, etc.).
But in a sense, you don't "owe" the money yet, because you haven't written back (they usually give you about three weeks to reply) confirming that you accept their change to the return - by which point you are very likely to have your refund. Give it another week - and be sure to answer that letter in a timely fashion - even if you can't pay it yet, the worst thing in the world is to NOT reply to an IRS letter.
