Yes i had to do that at the begining of my process and thats what actually took me longer.Not because i didnt have the money it was the debt collectordepending on how they operate some will give you a letter two day after payment but some don't until 30days. which i had to keep calling begging for the letter.that pissed me off.But as long as u can get them to work with you will be fine. U broker was probably counting on them not requesting you to pay off which i dont know why because fha loans are the only loans that dont require.you to pay off collection from my understanding. Im think you shoul be able to close.within 3 week is reasonable. But that why a good broker motto is under promise not over promise!!!I could be wrong but im just going by my experience.Im going with.fha and thats one of the most easiest and it took me 3months