Fannie Mae rejected my offer - no other offers - timetable?

[Fran Flanagan]

I had an offer in on a fannie mae home for about 20% below list. I didn't expect them to accept, but was hoping they'd counter. They rejected my offer. I've learned from the agent that no offers have been received yet. None during their first look and now we're about a week into the investor period with no other offers.

It's a cool house, but with the amount of work needed, it is not worth what they have it listed for, in my opinion.

Is it even worthwhile to increase my offer slightly or do I just need to wait for them to drop the price? Any guesses on how long they'll wait before dropping the price, if there are no other offers?

Is the lack of other offers simply due to other investors knowing that it's not worthwhile to put in low offers on fannie properties, prior to a price drop?