No realtor worth a damn will ever refuse to submit your offer unless it's completely unreasonable, like trying to offer $10k on a house priced at $100k. If you're trying to drop $5-10k because of your inspection results, your agent should get it done. If they don't want to, you should find a new agent. One agent told me this about foreclosures the woman and I were looking at: "You guys have great jobs and a place to live. You don't need to buy right now, but the bank needs to sell so the ball's in your court."
Yes, counter with a lower number. You're not under contract, you can offer whatever you want and they can refuse whatever they want. Right now with the state banks are in, most are not willing to refuse a reasonable offer for something that isn't selling.
I would do some property research. Find out exactly how long it's been on the market, what the owed balance was at that time, the rate of dollar decline from then till now, and the average asking prices for homes in that area of the same build year and type. Using those figures you should be able to come up with the offer that's most advantageous to you and most acceptable to the bank.
And thanks for the non-political thread. Nice to finally see one of those in the Vent.