The seller's disclosure should have had some indication of the age of the furnace and hot water heater. A furnace can run several thousand dollars, but a water heater is not very expensive. I assume you like this property and that is how you got to this point. Is it worth losing this property over five or ten thousand dollars?
If the age of the furnace and water heater was disclosed and those are your only issues you may not be able to walk away without penalty. If there are structural issues or things you cannot see that are revealed by the inspection then you are reasonably entitled to expect some equitable adjustment.
You state that you are paying a "high price", but I am not sure if that means top-dollar based on comparable homes in the neighborhood or you are just buying an expensive house. If you are buying at the top end of your budget and you don't have any "wiggle room" in your budget going forward that is not the seller's problem. If you are paying top-dollar then you can reasonably expect some concessions by the seller, but your agent should negotiate with the listing agent on these issues before you just walk away.
You state that there is an older hot water heater and furnace, and another little issue. Most sellers would be annoyed at this as the basis for a buyer wanting out of a contract. Many homeowners use appliances past their useful life per a published guideline. Most sellers and most agents will question what more is behind this buyer motivation. In and of itself, older mechanicals are not generally a cause for a deal to fall through.
Was a seller's disclosure provided for you? Did that include the age of the appliances?
Is there another reason why you do not wish to purchase this property? If the older mechanicals are your sole concern, and a seller will not pay for a home warranty for you, considering purchasing one yourself. The warranty may cost $400-$600/year depending upon the size of the property and what coverage you elect. For a set service call fee, your appliances and mechanicals in the property will be repaired. In many circumstances, an appliance will be replaced if it is not repairable for no additional fee. Service call fees range from $50-$80 depending upon the warranty provider, elected coverage and location.
You should first check what was said DURING attorney review. Some review letters specifically state that inspection "issues" do not include items which are functional, but "past their uselful life expectency".
Was there a sellers disclosure that you read and signed prior to making the offer? Did it disclose that the items in question were older? Even if it didn't or there was no disclosure, if an item is older but functional, you might be hard presesed to make the case to cancel the contract just because the items are older.
Also the purpose of an inspection is to make sure things are working correctly, tell you how they work, and tell you how old they are. Most inspectors only "suggest" budgeting for eventual replacement of older items. They don't recommend if its working for the sellers to provide you with new appliances, in essence leaving the house in better shape for you than when they lived there.
Doesn't it make sense that if the furnace or water heater were not functioning while the SELLERs are living there and needed replacement the sellers would have done that for their OWN confort???
If you like the house, why not just ask if the seller will purchase a home warranty for you. You agent can explain waht that is and what they cover. Worst case, you can always buy the home warranty for yourself after closing, which should give you opeace of mind about repairs until you are ready to replace the items.
It really bothers me that most buyers today want to buy a house but expect everything to be new when they move in. ALL homes eventually need repairs, replacemen, upgradest of items and quite frankly even NEW things periodically break. If you aren't prepared to do the routine things that every homeowner has to do when owning a home, then you shouldn't be buying a house.
Consult with your attorney with regard to the specific issues contained within your inspection report and ask for their advice with respect to your options for your contract to purchase.
If it is a home that you really like you may consider asking the seller to provide you with a one year home warranty.
I have to love that a home inspector suggests the need to replace a working anything. You should ask the inspector what the winning lottery numbers will be tomorrow.