They came to clean my furnace today and I was told I need a new one.Inside of the boiler is a cast iron tank.One of the bolts that hold it together is rusted and broken.It seems to me that it would only take replacing this bolt to fix the problem but I was told I need a new furnace.Does this sound correct?

Without actually seeing it... that rusted and broken bolt might likelty take a Herculean effort to remove it.Heavily rusted bolts literally almost become one with the surrounding metal. And if this in fact holds halves of a boiler together, leakage and corrosion between those halves might have already started making a good seal impossible. Then there is the safety aspect that under pressure even iff accomplished would still result in a boiler that is not safe to operate.

Clarification: You are stating furnace and boiler... do you have hot water (or steam) heat or forced air? By the sounds of it you have hot water heat which would be a boiler. Is the boiler leaking or is this just a recommendation from a preventive maintenance?