You're very fortunate to have found a hard money lender to lend you 80% of the rehab. Here in the D.C. area, it's generally 65%. In fact, even in "good" times it was never above 70%.
As another answer notes, hard money lenders now want you to have some "skin in the game." I work with one who only requires 5%; some require 10%.
Remember, too, that the hard money lender will be in first position. That means that whoever lends you 20% will be in second position--a very uncertain place to be.
OK: You might find some private lender out there willing to put up 10% of $65,000. That's $6,500. But unless you're talking about family or friends who'd just be doing you a favor, you'd probably be paying 20%-30% plus a few points--because of being in second position.
One other note: $65,000 overall isn't that much. Yes, it's real money. But if you're struggling over $13,000, maybe you should build up your reserves (perhaps by wholesaling a few deals) before doing a rehab.
Hope that helps.