@Brett Holmes - some of the other commenters have given good ideas.
I began real estate investing out of college with very little down payment funds, so I had to face these types of scenarios often.
Over the short-run you may need to give away part of your deal to a partner or pay a higher interest rate in order to get funds from a private lender and do a deal. But I'd rather have part of a deal than all of nothing, so over the long run it can be worth it while you save up funds to do it on your own.
The question is how to split the deal with someone in order to raise the down payment funds. You have a few choices, and in all cases you want to have full-disclosure to your bank lender about what you're trying. If they don't like it, move on to someone who does or use a different strategy:
1. You could do a traditional partnership with someone who has the 20% down. You could buy the house together. I don't like this scenario for only one deal because of the amount of work and trouble and administration and tax returns you'll need to deal with. If you're doing a lot of deals together, maybe that's ok. If it's only one deal, I'd prefer the next option.
2. Sell an option on the property to a private lender/partner. For example, this option could give them the right to buy 50% of the property for 50% of your purchase price for 10 years (or some length of time). Their option would be recorded in 2nd position behind the bank's. This isn't borrowed money. You have no payments. You're selling a future interest in your deal to a "partner" using an option. But there is no partnership tax return because you own it, you get the depreciation, you pay the mortgage, etc. The perfect lender is a self-directed IRA who has $10,000-20,000 sitting around doing nothing and who wants a passive deal.
I haven't tried this type of arrangement lately with conventional lenders. If they don't like it, perhaps try local banks and credit unions.
3. Let a credit-partner who DOES have the down payment buy the property, then you lease it back with the option to buy within a few years. You'd sublease the property to your own tenants to generate income. Your option price will be for a higher price than the purchase to give the credit partner an incentive to do this. Your lease to the credit partner would cover their payment, taxes, insurance, etc. For a long-term keeper, your goal would be to get a loan eventually and execute your option to purchase.
4. Try to negotiate a lease option or seller financing from a seller. Be sure to get help from a local attorney to prepare and record good documents to secure your investment. But you can often get in much lighter using this scenario while you save up a down payment for a refinance later.
Those are just some ideas. As someone else said, if you find a great deal - you can figure out a way to find the money. These are just a few ideas to get started.
I wrote an article here on BP about a Creative Financing Toolbox if you start to look more outside traditional financing.
Good luck!