Turns out the psychic was RIGHT when she said she saw somebody VERY SERIOUS about our house, and she felt they would come back with an offer. We held our ground, and figured the potential buyers from Sunday night were not gonna come up as much as we wanted (remember they originally offered us $30,000 less than we were asking). Then our realtor called yesterday to say that they were back with another offer (an additional $7000 from a previous offer) and a guarantee of same day closing -- July 8th.
Both parties have agreed on the terms and we now go to attorney review. The point is we did come down $16,000 and they came up $17,000 so I feel good about meeting in the middle.
It's going to be a long weekend in more ways than one. Now we hold our breath and hope that everything works out the next couple of days, and during the home inspection. But I definitely feel hopeful. Things look good.