Hi,
I would try to buy time on purchasing the home, if you can't get the time let the house go and look for another house in a couple of months.
This is my advice, because you can better start repairing your credit reports right now and improve your credit in the next few months. When you have better credit you will get a much better mortgage deal and that is something you will profit from for a long time.
If you really want the house and can not/ will not wait, pay the collection agency, let them sign a document that states they will remove the negative info upon payment and make sure they file this with the Credit Reporting Agencies as soon as possible.
Then just wait and hope it goes fast enough.
Hopefully this is helpful, good luck!!