As a former (and successful) realtor I would tell you to insist your realtor take her a written offer. Her realtor (if she wants to make the sale)should advise her client the first offer is 90% of the time the best and this market is very weak. There is at least a 9 month inventory right now of currently owned homes. That means if no other homes came on the market for the next 9 months there would be homes available to purchase! Also, the longer a home is on the market the harder it is to sell. Buyers wonder what is wrong with it.
Now to make you feel better, if this house isn't meant for you a better one is just out there waiting for you. If the lady is not ready to sell she can make the transaction miserable to say the least. I hope you have a strong realtor.
I am not sure what the laws are in your state but insist on a home inspection with a LICENSED inspector. Make sure you go to the inspection and follow the inspector around and ask questions. The more you know the better prepared you will be.
The inspection is sort of boring but it only lasts a couple of hours. In NJ if there are issues that the homeowner will not address you can rescend your offer with no cost to you except for the inspection fee. Your ernest money is returned in a few days. (In NJ, it is kept in an escrow account at YOUR realtor's company..I don't know how it is done in Michigan)