How would that work? How/why would you extend credit/financing to people with bad credit. BillMeLater is subject to credit approval.
This could be disastrous and a recipe for bankruptcy if not managed properly. My biggest concern with this software is what type of person is likely to finance a $100 purchase from NewEgg, certainly not someone with good credit I would hope. I only use BillMeLater because it's interest free so, however minimal, I get 6 months of interest I wouldn't have normally gotten if I had paid immediately. This doesn't sound like what the OP wants to do.
That said, I'd never NOT purchase because of a lack of BillMeLater or similar services so it's not like adding this feature would give you access to new customers.
What the OP proposes is basically a credit card company, it's not really disruptive. Neither was BillMeLater.
