Your best bet would be to find a Realtor and have them connect you to their lending source. The lending source, after running the credit will be able to plug in the many different compensating factors to assign an interest rate. The short answer is most lenders use a ratio to qualify. For example:
28/38 ratio. This means that the house payment can't exceed 28% of your GROSS income. In this case $1375 would be your number. And all other revolving debt (car payment, credit card, school loan etc..) including your house payment can't exceed 38% of your GROSS income. This is called a front end qualification and a back end qualification.
Depending on the lender, your credit, and the program they decide to qualify you on, the ratio can be adjusted. If you have a credit score over 750 they might base it on a 35/45 ratio. Some can go as high as 50% on the back end. Again it will depend on the lender.
The down payment is only fixed in one scenario. FHA. FHA loans require 3.5% minimum down. These are ALL variables in coming to a final answer.
Can someone qualify for a home on $55K? Yes. In San Diego...you might be looking at a condo.
I will give you a sample:
Case study - $165,000 property with an interest rate of 5% for a 30 year fixed loan period, considering 1.2% property tax, association dues of $250 per month, and property insurance of 1.5%, your house payment should fall around $1333 per month. This does not include PMI (private mortgage insurance) which you might need if you put less than 20% down (33K)
If you put 33K down one could effectively purchase a property for around $198K
Please understand these are just numbers off the top of my head and are in no way a guarantee.
However, a lender can give you what you are looking for.
Your lender will walk you through all of it.
Best of Luck!
Remax / Lakeland