Of course the YC connections were the first things on my mind. I don't think you can equate them to hard cash. It's just that the cash would have given me the chance to quit consulting and go 100% on my idea. But it's not the end of the world.
I know we could get $10k+ from other sources, but when it's not from a venture firm like YC and it's instead from our own savings and from friends/family like we have considered before, it's a lot harder to accept.
I doubt many people are just going to give up right now after rejection even (and especially) if they had a good idea, it's just that YC would have helped a ton.
It's a bit as if you're saying that it is easier to accept money from 'strangers'.
Personally I think that if your idea has merit and 10k is the big issue that you should get an extra job, save like the devil for the next 10 months to a year and then do it anyway. And face up to the fact that if 10k is the real problem that your idea may not have as much merit as you think after all.
I know this sounds quite harsh but good ideas + good teams are not going to go down because of a little bit of $.
I find any money hard to accept, stranger or not. To me, applying to YC (and all the possible consequences) was a harder decision than the decision to not accept friends/family money because it is from "strangers", and that's money I typically find hardest to accept.
However, while in a way preexisting relationships can be helpful, sometimes they can be a negative. I have lots of friends but not many that can honestly afford to chip in anywhere near that much (we're all entering that phase of student loans and new families). I have family but they usually want extortionate shares or interest in exchange (think like half of revenue for chipping in $20k at the beginning), plus the whole time provide the massive emotional burden of "you're a failure to this family if you don't succeed wildly". So given the alternatives, I'd prefer a more impartial stranger or group of strangers that don't do something like that, that can provide me with more than just money and a lot of international nagging.
That being said, I'd be stupid to think that $10k is a big issue. It's not, I hope it never comes to that, and I never have thought it to be at any point...in fact, this topic is the first time I even considered the idea of $10k or even $20k being a big issue, and I had to laugh at it. I have more than that in my savings alone, and although I like to have a little financial cushion at all times, I would consider using most of it for the startup if need be. It's just not money I can easily part with for the sake of working fulltime on the startup during the summer when the original pre-ycombinator plan was to do that anyway, just with some low maintenance/effort contract work on the side at the same time to take care of the small bills and inevitable money we'll need anyway.
That way you'll be able to do your thing
Why not just save some money for a few months (or however long it takes)? If you want it badly enough, waiting shouldn't be a problem...