REO offer with another bid?

We are purchasing a home for our family to live. Since we already own a home, the home we purchase will be an "investment" property. We are using a conventional loan w/ 20% down and no contingencies. We put an offer in on an REO property yesterday & were told today that there is another bid. They told us they are giving us and the other bidder the option to bid more. The home is listed at 135k, we offered 131k. It has been on the market for 3 months but they recently lowered the LP & fixed up the home to "move-in-able" condition. Are we being realistic in thinking we will get this property?