It's hard to say if you have a 50/50 shot or a 25% chance of your offer being accepted. There is no way of knowing the banks standpoint. They could have 1000 homes and need to get them off their books by the a certain time, so may take it just to get rid of it, or they could have so much tied up in it that they are willing to hold it till a better offer comes in.
Good luck, hopefully you'll be lucky and get a YES!!! (I've had banks accept offers 20% below market, so if that $189,900 is close to market, then $140,000 is only about 25% below market. But get a local Realtor - NOT the realtor listing the house - to help you determine market value.