How possible would it be to finance a rather cheap house?

yes of course theres a way! it sounds as if the banks/mortgage companies you are contacting just are not the right ones. If you have blemished credit there are still tons of places out there willing to lend you the money- some may want a down payment or minimal downpayment – but there are sometimes ways to work around that, you just need to get ahold of the right people. It makes no sense at all that they would be willing to lend you more – but not less. So that leads me to believe that possibley this home you want to buy needs work? if thats the case then you may have better luck looking either towards a government loan such as 203k if you qualify, and if not maybe towards a investor loan (hint google search hard money in your area). you might want to try country wide at 1-800-825-4549, or priority at 1-888-685-5885, or 813-473-4702. from my experiences none of these places have a minimum they will lend- but some of it depends on the home. If your credit is that bad- you may beed a small down payment. If in a couple of months you have exhausted your resources – then maybe you should work on getting your credit repaired.! here’s a site worth looking at if thats the case:.
good luck