Once the home has been sold at auction, the new owner is entitled to possession immediately; however, they can't lock you out. In order to evict you, they have to serve you with a 3 day notice to quit and then file a lawsuit for unlawful detainer. Only upon the new owner obtaining a court order / judgment for possession can they essentially lock you out. The unlawful detainer process is very fast. You only have 5 days after being served with the summons and complaint to respond. If you don't respond, they could have a writ of possession just over a week after they serve you with the summons by entering a default judgment. If you respond properly, the matter has to go to trial before they can get an order for possession. That only takes a few weeks, but there are ways to legally slow the process down in some cases.
I would also let you know that hiring a lawyer for a loan modification doesn't guarantee anything since there are no laws that force the lender to work with you. Lawyers know your rights and the process, but in many cases, the banks won't work with the lawyer either, the banks just don't really care.
It sounds like the new owner is willing to work with you to avoid the costs of eviction and give you some time to get out. You may want to negotiate a little more time and work with them.