The down-payment is one small part of a larger "qualify mortgage" question.
A mortgage lender wants three things from a potential customer: Steady income, a relatively clean recent credit history, and a debt-to-income ratio of 35% or less. Customers who qualify for a mortgage have all three of these qualities, plus a down-payment.
Start with Mortgage Basics to Know Before You Apply for a Loan. Next, I recommend you download a Uniform Residential Loan Application (Form 1003), complete it, and resume your mortgage shopping. Then, go to the Bills.com mortgage saving center for no-cost, pre-screened quotes from mortgage lenders.
Next, go to AnnualCreditReport.com to get a no-cost, no-obligation copy of your credit report from each of the three major consumer credit reporting companies (commonly called "credit bureaus"). Review your report and dispute any inaccurate listings.
To find out more how your credit score is calculated I recommend you read an article I wrote explaining FICO Score Calculation. This should give you a much clearer understanding of how credit scores work.
Finally, lenders calculate and analyze your debt-to-income ratio to determine the size of mortgage you can afford. See DTI: Debt-to-Income Ratio Information to learn how to calculate your debt-to-income ratio.
Given the amount you have available for a down payment, you should be able to qualify for a mortgage if you have a steady income and a low DTI.
I hope this information helps you Find. Learn & Save.